Martin SchechterProfessor, Mathematics |
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Research Interests |
Partial Differential Equations, Functional Analysis, Critical Point Theory, Operator Theory, Spectral and Scattering Theory, Quantum Mechanics | |
| URL | www.math.uci.edu/faculty/mschecht.html | |
| Publications | Schechter, Martin The use of Cerami sequences in critical point theory. Abstr. Appl. Anal. 2007, Art. ID 58948, 28 pp. | |
| Perera, Kanishka; Schechter, Martin Sandwich pairs in $p$-Laplacian problems. Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 29--34. | ||
| Schechter, Martin Semilinear problems in unbounded domains. J. Math. Anal. Appl. 327 (2007), no. 2, 1143--1154. | ||
| Schechter, Martin Sandwich pairs. Differential & difference equations and applications, 999--1007, Hindawi Publ. Corp., New York, 2006. | ||
| Schechter, Martin; Tintarev, Kyril Finding linking sets. Int. J. Math. Math. Sci. 2006, Art. ID 24623, 13 pp. (Reviewer: Silvia Cingolani) | ||
| Schechter, Martin Periodic solutions of second-order nonautonomous dynamical systems. Bound. Value Probl. 2006, Art. ID 25104, 9 pp. (Reviewer: Thomas Bartsch) | ||
| Schechter, M.; Zou, W. Sign-changing critical points from linking type theorems. Trans. Amer. Math. Soc. 358 (2006), no. 12, 5293--5318 (electronic). (Reviewer: Florica Corina \c St. Cîrstea) | ||
| Zou, Wenming; Schechter, Martin Critical point theory and its applications. Springer, New York, 2006. xii+318 pp. ISBN: 978-0-387-32965-9; 0-387-32965-X (Reviewer: James F. Reineck) | ||
| Schechter, Martin Periodic non-autonomous second-order dynamical systems. J. Differential Equations 223 (2006), no. 2, 290--302. (Reviewer: Shi Qing Zhang) | ||
| Schechter, Martin Critical point theory on unbounded regions. Comm. Appl. Nonlinear Anal. 13 (2006), no. 1, 97--105. (Reviewer: Shaowei Chen) | ||
| Schechter, Martin; Tintarev, Kyril Linking in Hilbert space. Proc. Amer. Math. Soc. 134 (2006), no. 2, 403--410 (electronic). (Reviewer: Miguel Ramos) | ||
| Schechter, Martin Saddle point techniques. Nonlinear Anal. 63 (2005), no. 5-7, 699--711. | ||
| Schechter, M.; Zou, W. Infinitely many solutions to perturbed elliptic equations. J. Funct. Anal. 228 (2005), no. 1, 1--38. (Reviewer: Yao Tian Shen) | ||
| Schechter, Martin Semilinear problems with bounded nonlinear term. Bound. Value Probl. 2005, no. 1, 1--8. | ||
| Schechter, Martin An introduction to nonlinear analysis. Cambridge Studies in Advanced Mathematics, 95. Cambridge University Press, Cambridge, 2004. xviii+357 pp. ISBN: 0-521-84397-9 (Reviewer: Patricio L. Felmer) | ||
| Schechter, Martin; Zou, Wenming The method of weak linking. Abstract and applied analysis, 323--334, World Sci. Publ., River Edge, NJ, 2004. (Reviewer: Andrzej Szulkin) | ||
| Schechter, Martin; Zou, Wenming An infinite-dimensional linking theorem and applications. J. Differential Equations 201 (2004), no. 2, 324--350. (Reviewer: Marco Squassina) | ||
| Schechter, M.; Wang, Z.-Q.; Zou, W. New linking theorem and sign-changing solutions. Comm. Partial Differential Equations 29 (2004), no. 3-4, 471--488. (Reviewer: Florica Corina \c St. Cîrstea) | ||
| Schechter, Martin; Zou, Wenming Superlinear problems. Pacific J. Math. 214 (2004), no. 1, 145--160. (Reviewer: Régis Monneau) | ||
| Schechter, Martin; Zou, Wenming Weak linking. Nonlinear Anal. 55 (2003), no. 6, 695--706. (Reviewer: Kanishka S. Perera) | ||
| Schechter, M.; Zou, W. Double linking theorem and multiple solutions. J. Funct. Anal. 205 (2003), no. 1, 37--61. (Reviewer: Monica Musso) | ||
| Schechter, Martin; Zou, Wenming Weak linking theorems and Schrödinger equations with critical Sobolev exponent. ESAIM Control Optim. Calc. Var. 9 (2003), 601--619 (electronic). (Reviewer: Luisa Moschini) | ||
| Tszou, V.; Shekhter, M. On functions bounded from below. (Russian) Funktsional. Anal. i Prilozhen. 37 (2003), no. 2, 75--80, 96; translation in Funct. Anal. Appl. 37 (2003), no. 2, 142--146 (Reviewer: Dumitru Motreanu) | ||
| Perera, Kanishka; Schechter, Martin Computation of critical groups in Fu\v cík resonance problems. J. Math. Anal. Appl. 279 (2003), no. 1, 317--325. (Reviewer: Monica Lazzo) | ||
| Perera, Kanishka; Schechter, Martin Double resonance problems with respect to the Fu\v cík spectrum. Indiana Univ. Math. J. 52 (2003), no. 1, 1--17. (Reviewer: Bryan P. Rynne) | ||
| Schechter, Martin; Zou, Wenming Homoclinic orbits for Schrödinger systems. Michigan Math. J. 51 (2003), no. 1, 59--71. (Reviewer: Vassilios M. Rothos) | ||
| Schechter, Martin Operator methods in quantum mechanics. Reprint of the 1981 original. Dover Publications, Inc., Mineola, NY, 2002. xxii+324 pp. ISBN: 0-486-42547-9 | ||
| Perera, Kanishka; Schechter, Martin Critical groups in saddle point theorems without a finite dimensional closed loop. Math. Nachr. 243 (2002), 156--164. (Reviewer: Monica Musso) | ||
| Schechter, Martin Some recent results in critical point theory. Panamer. Math. J. 12 (2002), no. 2, 1--19. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin Principles of functional analysis. Second edition. Graduate Studies in Mathematics, 36. American Mathematical Society, Providence, RI, 2002. xxii+425 pp. ISBN: 0-8218-2895-9 (Reviewer: R. G. Bartle) | ||
| Perera, Kanishka; Schechter, Martin Solution of nonlinear equations having asymptotic limits at zero and infinity. Calc. Var. Partial Differential Equations 12 (2001), no. 4, 359--369. (Reviewer: Fabiana Leoni) | ||
| Perera, Kanishka; Schechter, Martin Applications of Morse theory to the solution of semilinear problems depending on $C\sp 1$ functionals. Nonlinear Anal. 45 (2001), no. 1, Ser. A: Theory Methods, 1--9. (Reviewer: Marco Squassina) | ||
| Perera, Kanishka; Schechter, Martin The Fu\v cík spectrum and critical groups. Proc. Amer. Math. Soc. 129 (2001), no. 8, 2301--2308 (electronic). (Reviewer: Xiaofeng Ren) | ||
| Schechter, Martin Periodic solutions of semilinear higher dimensional wave equations. Chaos Solitons Fractals 12 (2001), no. 6, 1029--1034. | ||
| Schechter, Martin Multiple solutions for semilinear elliptic problems. Mathematika 47 (2000), no. 1-2, 307--317 (2002). (Reviewer: Gabriella Tarantello) | ||
| Perera, Kanishka; Schechter, Martin A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities. NoDEA Nonlinear Differential Equations Appl. 7 (2000), no. 4, 361--367. (Reviewer: João Marcos Bezerra do Ó) | ||
| Perera, Kanishka; Schechter, Martin Multiple nontrivial solutions of elliptic semilinear equations. Topol. Methods Nonlinear Anal. 16 (2000), no. 1, 1--15. (Reviewer: Yong Qing Li) | ||
| Schechter, Martin Resonance problems with respect to the Fu\v cík spectrum. Trans. Amer. Math. Soc. 352 (2000), no. 9, 4195--4205 (electronic). (Reviewer: Jie Yang) | ||
| Perera, Kanishka; Schechter, Martin Nontrivial solutions of elliptic semilinear equations at resonance. Manuscripta Math. 101 (2000), no. 3, 301--311. (Reviewer: Gianni Arioli) | ||
| Perera, Kanishka; Schechter, Martin Semilinear elliptic equations having asymptotic limits at zero and infinity. Abstr. Appl. Anal. 4 (1999), no. 4, 231--242. (Reviewer: David Arcoya) | ||
| Schechter, Martin Linking methods in critical point theory. Birkhäuser Boston, Inc., Boston, MA, 1999. xviii+294 pp. ISBN: 0-8176-4095-9 (Reviewer: Jean-Noël Corvellec) | ||
| Perera, Kanishka; Schechter, Martin Type II regions between curves of the Fu\v cik spectrum and critical groups. Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 227--243. (Reviewer: Jie Yang) | ||
| Schechter, Martin Rotationally invariant periodic solutions of semilinear wave equations. Abstr. Appl. Anal. 3 (1998), no. 1-2, 171--180. (Reviewer: Eduard Feireisl) | ||
| Perera, Kanishka; Schechter, Martin Morse index estimates in saddle point theorems without a finite-dimensional closed loop. Indiana Univ. Math. J. 47 (1998), no. 3, 1083--1095. (Reviewer: Maria Letizia Bertotti) | ||
| Schechter, Martin Infinite-dimensional linking. Duke Math. J. 94 (1998), no. 3, 573--595. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin Critical point theory with weak-to-weak linking. Comm. Pure Appl. Math. 51 (1998), no. 11-12, 1247--1254. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin New linking theorems. Rend. Sem. Mat. Univ. Padova 99 (1998), 255--269. (Reviewer: Jean Mawhin) | ||
| Schechter, Martin Eigenvalue problems for semilinear equations. Spectral and scattering theory (Newark, DE, 1997), 157--175, Plenum, New York, 1998. (Reviewer: Wen Xiong Chen) | ||
| Schechter, Martin Type (II) regions between curves of the Fucik spectrum. NoDEA Nonlinear Differential Equations Appl. 4 (1997), no. 4, 459--476. (Reviewer: Jesús Hernández) | ||
| Schechter, Martin Resonance problems which intersect many eigenvalues. Math. Nachr. 183 (1997), 201--210. (Reviewer: Marco Degiovanni) | ||
| Schechter, Martin New techniques in critical point theory. Partial differential equations and applications, 289--294, Lecture Notes in Pure and Appl. Math., 177, Dekker, New York, 1996. (Reviewer: Dorin Andrica) | ||
| Schechter, M.; Tintarev, K. Critical points for pairs of functionals and semilinear elliptic equations. Calculus of variations, applications and computations (Pont-à-Mousson, 1994), 245--253, Pitman Res. Notes Math. Ser., 326, Longman Sci. Tech., Harlow, 1995. (Reviewer: J. V. A. Gonçalves) | ||
| Schechter, Martin Critical points when there is no saddle point geometry. Topol. Methods Nonlinear Anal. 6 (1995), no. 2, 295--308. (Reviewer: Jean-Noël Corvellec) | ||
| Schechter, Martin The intrinsic mountain pass. Pacific J. Math. 171 (1995), no. 2, 529--544. (Reviewer: Jean-Noël Corvellec) | ||
| Schechter, Martin The saddle point alternative. Amer. J. Math. 117 (1995), no. 6, 1603--1626. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin Bounded resonance problems for semilinear elliptic equations. Nonlinear Anal. 24 (1995), no. 10, 1471--1482. (Reviewer: Rolando Magnanini) | ||
| Schechter, Martin Superlinear elliptic boundary value problems. Manuscripta Math. 86 (1995), no. 3, 253--265. (Reviewer: Wen Xiong Chen) | ||
| Berger, Melvyn; Schechter, Martin; Sun, Guo Zhang Infinite-dimensional singularity theory and bifurcation from equilibria for certain nonlinear evolution equations. Topol. Methods Nonlinear Anal. 4 (1994), no. 2, 341--353. (Reviewer: Jesús Hernández) | ||
| Schechter, Martin The Fu\v cík spectrum. Indiana Univ. Math. J. 43 (1994), no. 4, 1139--1157. (Reviewer: Yi Hong Du) | ||
| Schechter, Martin Elliptic resonance problems with unequal limits at infinity. Math. Ann. 300 (1994), no. 4, 629--642. (Reviewer: Mario M. Coclite) | ||
| Schechter, Martin The Hampwile alternative. Comm. Appl. Nonlinear Anal. 1 (1994), no. 4, 13--46. (Reviewer: Norman Dancer) | ||
| Schechter, Martin Asymptotically linear elliptic boundary value problems. Monatsh. Math. 117 (1994), no. 1-2, 121--137. (Reviewer: Xi Ping Zhu) | ||
| Schechter, Martin Landesman-Lazer resonance problems and saddle point methods. Math. Methods Appl. Sci. 17 (1994), no. 4, 229--238. (Reviewer: Xi Ping Zhu) | ||
| Schechter, Martin Strong resonance problems for elliptic semilinear boundary value problems. J. Operator Theory 30 (1993), no. 2, 301--314. (Reviewer: Alexander A. Pankov) | ||
| Schechter, Martin Splitting subspaces and saddle points. Appl. Anal. 49 (1993), no. 1-2, 33--48. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin Semilinear boundary value problems of the strong resonance type. Topol. Methods Nonlinear Anal. 2 (1993), no. 2, 189--202. (Reviewer: J. V. A. Gonçalves) | ||
| Schechter, Martin New saddle point theorems. Generalized functions and their applications (Varanasi, 1991), 213--219, Plenum, New York, 1993. (Reviewer: Norman Dancer) | ||
| Schechter, M.; Tintarev, K. Nonlinear eigenvalues and mountain pass methods. Topol. Methods Nonlinear Anal. 1 (1993), no. 2, 183--201. (Reviewer: Yi Hong Du) | ||
| Schechter, Martin Critical points over splitting subspaces. Nonlinearity 6 (1993), no. 3, 417--427. (Reviewer: Jean Mawhin) | ||
| Schechter, Martin; Tintarev, Kyril Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems. Bull. Soc. Math. Belg. Sér. B 44 (1992), no. 3, 249--261. (Reviewer: Miguel Ramos) | ||
| Schechter, Martin A generalization of the saddle point method with applications. Ann. Polon. Math. 57 (1992), no. 3, 269--281. (Reviewer: Marco Degiovanni) | ||
| Schechter, Martin The mountain cliff theorem. Differential equations and mathematical physics (Birmingham, AL, 1990), 263--279, Math. Sci. Engrg., 186, Academic Press, Boston, MA, 1992. (Reviewer: Jean Mawhin) | ||
| Schechter, Martin A bounded mountain pass lemma without the (PS) condition and applications. Trans. Amer. Math. Soc. 331 (1992), no. 2, 681--703. (Reviewer: Jean Mawhin) | ||
| Schechter, Martin A variation of the mountain pass lemma and applications. J. London Math. Soc. (2) 44 (1991), no. 3, 491--502. (Reviewer: William K. Ziemer) | ||
| Schechter, Martin; Tintarev, Kyril Points of spherical maxima and solvability of semilinear elliptic equations. Canad. J. Math. 43 (1991), no. 4, 825--831. (Reviewer: Yi Hong Du) | ||
| Schechter, Martin A saddle point theorem applied to semilinear boundary value problems. Panamer. Math. J. 1 (1991), no. 2, 1--25. (Reviewer: Jean Mawhin) | ||
| Schechter, Martin; Tintarev, Kyril Families of "first eigenfunctions" for semilinear elliptic eigenvalue problems. Duke Math. J. 62 (1991), no. 2, 453--465. (Reviewer: Claude Do) | ||
| Schechter, Martin The mountain pass alternative. Adv. in Appl. Math. 12 (1991), no. 1, 91--105. (Reviewer: Norman Dancer) | ||
| Schechter, Martin Solution of nonlinear problems at resonance. Indiana Univ. Math. J. 39 (1990), no. 4, 1061--1080. (Reviewer: Paolo Acquistapace) | ||
| Schechter, Martin; Tintarev, Kyril Eigenvalues for semilinear boundary value problems. Arch. Rational Mech. Anal. 113 (1990), no. 3, 197--208. (Reviewer: Ricardo S. Kubrusly) | ||
| Berger, M. S.; Schechter, M. Bifurcation from equilibria for certain infinite-dimensional dynamical systems. Mathematics of nonlinear science (Phoenix, AZ, 1989), 133--138, Contemp. Math., 108, Amer. Math. Soc., Providence, RI, 1990. (Reviewer: Jesús Hernández) | ||
| Schechter, Martin; Tintarev, Kyril Spherical maxima in Hilbert space and semilinear elliptic eigenvalue problems. Differential Integral Equations 3 (1990), no. 5, 889--899. (Reviewer: Zuchi Chen) | ||
| Schechter, Martin Nonlinear elliptic boundary value problems at strong resonance. Amer. J. Math. 112 (1990), no. 3, 439--460. (Reviewer: R. Kent Nagle) | ||
| Schechter, Martin Nonlinear elliptic boundary value problems at resonance. Nonlinear Anal. 14 (1990), no. 10, 889--903. (Reviewer: R. Kent Nagle) | ||
| Schechter, Martin The Hampwile theorem for nonlinear eigenvalues. Duke Math. J. 59 (1989), no. 2, 325--335. (Reviewer: E. Tarafdar) | ||
| Schechter, Martin Multiplication operators. Canad. J. Math. 41 (1989), no. 2, 234--249. (Reviewer: Ron Kerman) | ||
| Schechter, Martin The spectrum of the Schrödinger operator. Trans. Amer. Math. Soc. 312 (1989), no. 1, 115--128. (Reviewer: Hitoshi Kitada) | ||
| Schechter, Martin Boundary value problems for semilinear elliptic equations of arbitrary order in unbounded domains. Rocky Mountain J. Math. 18 (1988), no. 3, 519--534. (Reviewer: D. E. Edmunds) | ||
| Schechter, Martin Exact estimates for potentials. SIAM J. Math. Anal. 19 (1988), no. 6, 1324--1328. (Reviewer: Yoshimi Sait\=o) | ||
| Schechter, M.; Whitley, Robert Best Fredholm perturbation theorems. Studia Math. 90 (1988), no. 3, 175--190. (Reviewer: Jaroslav Zemánek) | ||
| Schechter, Martin Weighted norm inequalities for potential operators. Trans. Amer. Math. Soc. 308 (1988), no. 1, 57--68. (Reviewer: L. Losonczi) | ||
| Schechter, Martin Potential estimates in Orlicz spaces. Pacific J. Math. 133 (1988), no. 2, 381--399. (Reviewer: Bruno Franchi) | ||
| Schechter, Martin Weighted norm estimates for Sobolev spaces. Trans. Amer. Math. Soc. 304 (1987), no. 2, 669--687. (Reviewer: Yu. A. Brudny\u\i) | ||
| Schechter, Martin Semilinear boundary value problems for unbounded domains. Michigan Math. J. 34 (1987), no. 1, 63--76. (Reviewer: J. Ka\v cur) | ||
| Schechter, Martin Two space scattering and propagative systems. Illinois J. Math. 31 (1987), no. 1, 62--88. (Reviewer: J. Weidmann) | ||
| Schechter, Martin Spectra of partial differential operators. Second edition. North-Holland Series in Applied Mathematics and Mechanics, 14. North-Holland Publishing Co., Amsterdam, 1986. xiv+310 pp. ISBN: 0-444-87822-X (Reviewer: A. Devinatz) | ||
| Schechter, Martin Derivatives of mappings with applications to nonlinear differential equations. Trans. Amer. Math. Soc. 293 (1986), no. 1, 53--69. (Reviewer: Péter Tallós) | ||
| Schechter, Martin Selfadjoint operators, spectral and scattering theory, variational techniques, nonlinear phenomena, linear and nonlinear partial differential equations, and related topics. Differential equations (Birmingham, Ala., 1983), 501--509, North-Holland Math. Stud., 92, North-Holland, Amsterdam, 1984. | ||
| Schechter, Martin Differentiation in abstract spaces. J. Differential Equations 55 (1984), no. 3, 330--345. (Reviewer: A. B. Németh) | ||
| Schechter, Martin Imbedding estimates involving new norms and applications. Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 163--166. (Reviewer: J. S. Martins) | ||
| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=2165 | |
| Last updated | 10/18/2007 | |