Martin Schechter

Professor, Mathematics
School of Physical Sciences

PH.D., New York University, 1957

Phone: (949) 824-5501
Fax: (949) 824-7993
Email: mschecht@math.uci.edu

University of California, Irvine
540A Rowland Hall
Mail Code: 3875
Irvine, CA 92697


Research
Interests
Partial Differential Equations, Functional Analysis, Critical Point Theory, Operator Theory, Spectral and Scattering Theory, Quantum Mechanics
   
URL Professor Martin Schechter
   
Academic
Distinctions
NSF Senior Postdoctoral Fellowship, 1965-66

Member, Institute for Advanced Study, Princeton

Outstanding Teaching Award, UCI, 1986

Invited plenary speaker at the Joint the National Academy of Sciences - Soviet Academy of Sciences Symposium on Partial Differential Equations, Novosibirsk, 1963

Invited keynote speaker at the World Congress of Nonlinear Analysts, Orlando, Florida, 2004
   
Publications 1. (with Bers, L. and John, F.) Partial Differential Equations, Interscience, New York, 1964. American Mathematical Society, 1979
   
  2. Principles of Functional Analysis, Academic Press, New York, 1971. Second Edition, American Mathematical Society, 2002.
   
  3. Spectra of Partial Differential Operators, North Holland, Amsterdam, 1971. Second Edition 1986.
   
  4. Modern Methods in Partial Differential Equations, McGraw-Hill, New York, 1977.
   
  5. Operator Methods in Quantum Mechanics, Elsevier North-Holland, New York, 1981; Dover Publications, 2002.
   
  6. Linking Methods in Critical Point Theory, Birkh\'auser, Boston, 1999.
   
  7. An Introduction to Nonlinear Analysis. Cambridge Studies in Advanced Mathematics, 95. Cambridge University Press, Cambridge, 2004.
   
  8. (with W. Zou) Critical point theory and its applications. Springer, New York, 2006.
   
  9. Minimax Systems and Critical Point theory, Birkh\'auser, Boston, 2009.
   
  221. Schechter, M.; Zou, W. (2010). On the Brézis-Nirenberg problem.
Arch. Ration. Mech. Anal. 197, no. 1, 337–356.
50% contribution
220. Schechter, M. (2010). Monotonicity methods for infinite dimensional sandwich
systems. Discrete Contin. Dyn. Syst. 28, no. 2, 455–468.
219. Schechter, M. (2010). The use of core functions in semilinear problems.
Comm. Appl. Nonlinear Anal. 17, no. 1, 93–102
218. Schechter, M. (2010). Variant sandwich pairs. Math. Nachr. 283, no. 2, 272– 288.
217. Schechter, M. (2009). Applications of sandwich pairs. Nonlinear Anal. 71, no. 12, 234–242.
216. Schechter, M. (2009). Linking sandwich pairs.
Math. Proc. Cambridge Philos. Soc. 147, no. 3, 679–700.
215. Schechter, M. (2009). Wave equations that are radially symmetric.
Commun. Appl. Anal. 13, no. 3, 287–292.
214. Schechter, M., Perera, K. (2009). Sandwich pairs for p-Laplacian systems.
J. Math. Anal. Appl. 358, no. 2, 485–490.
50% contribution
212. Schechter, M. (2009). Custom sandwich pairs. J. Differential Equations 246, no. 8, 3398–3415.
211. Schechter, M. (2009). Systems of sandwich pairs. J. Fixed Point Theory Appl. 5, no. 1, 145–155.
210. Schechter, M., Perera, K. (2008). Flows and critical points. NoDEA Nonlinear Differential Equations Appl, 15(4-50), 495-509.
50% contribution
209. Schechter, M. (2008). Critical point methods. Nonlinear Anal., 69(3), 987-999.
208. Schechter, M. (2008). Strong sandwich pairs. Indiana Univ. Math. J., 57(3), 1105-1131.
207. Schechter, M. (2008). Minimax systems. J. Math Anal. Appl, 345, 431-454.
206. Schechter, M. (2008). Infinite-dimensional sandwich pairs. Pacific J. Math., 235(1), 73-88.
205. Schechter, M. (2008). Sandwich pairs in critical point theory. Trans. Amer. Math. Soc., 360(6), 2811-2823.
203. Schechter, M. (2007). The use of Cerami sequences in critical point theory. Abstr. Appl. Anal., 28 pp.
202. Schechter, M., Perera, K. (2007). Sandwich pairs in $p$-Laplacian problems. Topol. Methods Nonlinear Anal., 29(1), 29-34.
50% contribution
201. Schechter, M. (2007). Semilinear problems in unbounded domains. J. Math. Anal. Appl., 327(2), 1143-1154.
199. Schechter, M. (2006). Periodic solutions of second-order nonautonomous dynamical systems. Bound. Value Probl., 9pp.
198. Schechter, M., Zou, W. (2006). Sign-changing critical points from linking type theorems. Trans. Amer. Math. Soc., 358(12), 5293-5318.
50% contribution
196. Schechter, M. (2006). Periodic non-autonomous second-order dynamical systems. J. Differential Equations, 223(2), 290-302.
195. Schechter, M. (2006). Critical point theory on unbounded regions. Comm. Appl. Nonlinear Anal., 13(1), 97-105.
194. Schechter, M., Tintarev, K. (2006). Finding linking sets. Int. J. Math. Math. Sci., 13pp.
50% contribution
193. Schechter, M., Tintarev, K. (2006). Linking in Hilbert space. Proc. Amer. Math. Soc., 134(2), 403-410.
50% contribution
192. Schechter, M. (2005). Saddle point techniques. Nonlinear Anal., 63(5-7), 699-711.
191. Schechter, M. (2005). Infinitely many solutions to perturbed elliptic equations. J. Funct. Anal., 228(1), 1-38.
190. Schechter, M. (2005). Semilinear problems with bounded nonlinear term. Bound. Value Probl., 1, 1-8.
188. Schechter, M., Zou, W. (2004). The method of weak linking. Abstract and applied analysis, 323-334.
50% contribution
187. Schechter, M., Zou, W. (2004). An infinite-dimensional linking theorem and applications. J. Differential Equations, 201(2), 324-350.
50% contribution
186. Schechter, M., Zou, W. (2004). Super-linear problems. Pacific J. Math, 214(1), 145-160.
50% contribution
185. Schechter, M., Zou, W. (2003). Weak linking. Nonlinear Anal., 55(6), 695-706.
50% contribution
184. Schechter, M., Wang, Z. Q., Zou, W. (2004). New linking theorem and sign-changing solutions. Comm. Partial Differential Equations, 29(3-4), 471-488.
33% contribution
183. Schechter, M., Zou, W. (2003). Double linking theorem and multiple solutions. J. Funct. Anal., 205(1), 37-61.
50% contribution
182. Schechter, M., Zou, W. (2003). Weak linking theorems and Schrödinger equations with critical Sobolev exponent. ESAIM Control Optim. Calc. Var., 9, 601--619.
50% contribution
181. Schechter, M., Zou, W. (2003). On functions bounded from below. Funktsional. Anal. i Prilozhen., 37(2), 75--80, 96. (Russian).
50% contribution
180. Schechter, M., Perera, K. (2003). Computation of critical groups in Fu\v cík resonance problems. J. Math. Anal. Appl., 279(1), 317—325.
50% contribution
179. Schechter, M., Perera, K. (2003). Double resonance problems with respect to the Fu\v cík spectrum. Indiana Univ. Math. J., 52(1), 1-17.
50% contribution
178. Schechter, M., Zou, W. (2003). Homoclinic orbits for Schrödinger systems. Michigan Math. J., 51(1), 59-71.
50% contribution
176. Schechter, M., Perera, K. (2002). Critical groups in saddle point theorems without a finite dimensional closed loop. Math. Nachr., 243, 156-164.
50% contribution
175. Schechter, M. (2002). Some recent results in critical point theory. Panamer. Math. J., 12(2), 1-19.
173. Schechter, M. (2002). Multiple solutions for semilinear elliptic problems. Mathematika, 47(1-2), 307-317.
172. Schechter, M. (2001). Periodic solutions of semilinear higher dimensional wave equations. Chaos Solitons & Fractals, 12(6), 1029-1034.
171. Schechter, M., Perera, K. (2001). Solution of nonlinear equations having asymptotic limits at zero and infinity. Calc. Var. Partial Differential Equations, 12(4), 359-369.
50% contribution
170. Schechter, M., Perera, K. (2001). Applications of Morse theory to the solution of semilinear problems depending on $C\sp 1$ functionals. Nonlinear Anal., 45(1, Ser. A: Theory Methods, 1-9).
50% contribution
169. Schechter, M., Perera, K. (2001). The Fu\v cík spectrum and critical groups. Proc. Amer. Math. Soc., 129(8), 2301-2308.
50% contribution
168. Schechter, M., Perera, K. (2000). Multiple nontrivial solutions of elliptic semilinear equations. Topol. Methods Nonlinear Anal., 16(1), 1-15.
50% contribution
167. Schechter, M., Perera, K. (2000). A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities. NoDEA Nonlinear Differential Equations Appl., 7(4), 361-367.
50% contribution
166. Schechter, M., Perera, K. (2000). Nontrivial solutions of elliptic semilinear equations at resonance. Manuscripta Math., 101(3), 301--311.
50% contribution
165. Schechter, M. (2000). Resonance problems with respect to the Fu\v cík spectrum. Trans. Amer. Math. Soc., 352(9), 4195-4205.
164. Schechter, M., Perera, K. (1999). Semilinear elliptic equations having asymptotic limits at zero and infinity. Abstr. Appl. Anal., 4(4), 231-242.
50% contribution
163. Schechter, M., Perera, K. (1998). Type II regions between curves of the Fu\v cik spectrum and critical groups. Topol. Methods Nonlinear Anal., 12(2), 227-243.
50% contribution
162. Schechter, M. (1998). Rotationally invariant periodic solutions of semilinear wave equations. Abstr. Appl. Anal., 3(1-2), 171-180.
161. Schechter, M., Perera, K. (1998). Morse index estimates in saddle point theorems without a finite-dimensional closed loop. Indiana Univ. Math. J., 47(3), 1083-1095.
50% contribution
160. Schechter, M. (1998). Infinite-dimensional linking. Duke Math. J., 94(3), 573--595.
159. Schechter, M. (1998). Critical point theory with weak-to-weak linking. Comm. Pure Appl. Math., 51(11-12), 1247-1254.
158. Schechter, M. (1997). Resonance problems which intersect many eigenvalues. Math. Nachr., 183, 201-210.
157. Schechter, M. (1997). Type (II) regions between curves of the Fucik spectrum. NoDEA Nonlinear Differential Equations Appl., 4(4), 459-476.
155. Schechter, M. (1998). New linking theorems. Rend. Sem. Mat. Univ. Padova, 99, 255-269.
154. Schechter, M. (1995). Critical points when there is no saddle point geometry. Topol. Methods Nonlinear Anal., 6(2), 295-308.
152. Schechter, M. (1995). The intrinsic mountain pass. Pacific J. Math., 171(2), 529-544.
151. Schechter, M. (1995). The saddle point alternative. Amer. J. Math., 117(6), 1603-1626.
149. Schechter, M. (1995). Superlinear Elliptic Boundary Value Problems. Manuscripta Mathematica, 86, 253-265.
148. Schechter, M. (1995). Bounded Resonance Problems for Semilinear Elliptic Equations. Nonlinear Analysis, Theory, Methods and Applications, 24, 1471-1482.
147. Schechter, M., Berger, M. S., Sun, G. Z. (1994). Infinite-dimensional singularity theory and bifurcation from equilibria for certain nonlinear evolution equations. Topological Methods in Nonlinear Analysis, 4(2), 341-353.
33% contribution
146. Schechter, M. (1994). Elliptic resonance problems with unequal limits at infinity. Math. Ann., 300(4), 629--642.
145. Schechter, M. (1994). The Fucik Spectrum. Indiana University Mathematics Journal, 43, 1139-1157.
144. Schechter, M. (1994). Landesman-Lazer Resonance Problems and Saddle Point Methods. Mathematical Methods in the Applied Sciences, 17, 229-238.
143. Schechter, M. (1994). The Hampwile Alternative. Communications in Applied Nonlinear Analysis, 1, 13-46.
142. Schechter, M. (1994). Asysmptotically Linear Elliptic Boundary Value Problems. Monatshefte fur Mathematik, 117, 121-137.
141. Schechter, M. (1993). Strong Resonance Problems for Elliptic Semilinear Boundary Value Problems. Journal of Operator Theory, 30, 301-314.
140. Schechter, M. (1993). Semilinear Boundary Value Problems of the Strong Resonance Type. Topological Methods in Nonlinear Analysis, 2, 189-202.
139. Schechter, M., Tintarev, K. (1993). Nonlinear Eigenvalues and Mountain Pass Methods. Topological Methods in Nonlinear Analysis, 1, 183-201.
50% contribution
138. Schechter, M. (1993). Splitting Subspaces and Saddle Points. Applicable Analysis, 49, 33-48.
137. Schechter, M. (1993). Critical Points Over Splitting Subspaces. Nonlinearity, 6, 417-427.
136. Schechter, M. (1993). New saddle point theorems. Generalized functions and their applications, 213-219.
135. Schechter, M. (1992). A Generalization of the Saddle Point Method with Applications. Annales Polonici Mathematici, 57, 269-281.
134. Schechter, M., Tintarev, K. (1992). Pairs of Critical Points Produced by Linking Subsets with Applications to Semilinear Elliptic Problems. Bulletin de la Societe Mathematique de Belgique, 44, 249-261.
50% contribution
133. Schechter, M. (1992). A Bounded Mountain Pass Lemma Without the (PS) Condition and Applications. Transactions of the American Mathematical Society, 331, 681-703.
132. Schechter, M., Tintarev, K. (1991). Points of spherical maxima and solvability of semilinear elliptic equations. Canad. J. Math., 43(4), 825-831.
50% contribution
131. Schechter, M. (1991). A Variation of the Mountain Pass Lemma and Applications. Journal of the London Mathematical Society, 44, 491-502.
130. Schechter, M. (1991). A Saddle Point Theorem Applied to Semilinear Boundary Value Problems. Panamerican Mathematical Journal, 1(2), 1-25.
129. Schechter, M. (1992). The Mountain Cliff Theorem, Differential Equations and Mathematical Physics. Mathematics in Science and Engineering, 186, 263-279.
128. Schechter, M., Tintarev, K. (1991). Families of First Eigenfunctions for Semilinear Elliptic Eigenvalue Problems. Duke Mathematical Journal, 62, 453-465.
50% contribution
127. Schechter, M. (1991). The Mountain Pass Alternative. Advances in Applied Mathematics, 12, 91-105.
126. Schechter, M., Tintarev, K. (1991). Eigenvalues for Semilinear Boundary Value Problems. Archives of Rational Mechanics and Analysis, 113, 197-208.
50% contribution
125. Schechter, M. (1990). Solution of Nonlinear Problems at Resonance. Indiana University Mathematics Journal, 39, 1061-1080.
124. Schechter, M., Berger, M. S. (1990). Bifurcation from equilibria for Certain Infinite-Dimensional Dynamical Systems. Contemporary Mathematics, 108, 133-138.
50% contribution
123. Schechter, M. (1990). Nonlinear Elliptic Boundary Value Problems at Strong Resonance. American Journal of Mathematics, 112, 439-460.
122. Schechter, M., Tintarev, K. (1990). Spherical Maxima in Hilbert Space and Semilinear Elliptic Eigenvalue Problems. Differential and Integral Equations, 3, 889-899.
50% contribution
121. Schechter, M. (1990). Nonlinear Elliptic Boundary Value Problems at Resonance. Nonlinear Analysis, Theory, Methods and Applications, 14, 889-903.
120. Schechter, M. (1989). The Hampwile Theorem for Nonlinear Eigenvalues. Duke Mathematical Journal, 59, 325-335.
119. Schechter, M. (1989). The Spectrum of the Schrodinger Operator. Transactions of the American Mathematical Society, 312, 115-128.
118. Schechter, M. (1989). Multiplication Operators. Canadian Journal of Mathematics, 61, 234-249.
117. Schechter, M., Whitley, R. (1988). Best Fredholm Perturbation Theorems. Studia Mathematica, 90, 175-190.
50% contribution
116. Schechter, M. (1988). Exact Estimates for Potentials. SIAM Journal on Mathematical Analysis, 19, 1324-1328.
115. Schechter, M. (1988). Weighted Norm Inequalities for Potential Operators. Transaction of the American Mathematical Society, 308, 57-68.
114. Schechter, M. (1988). Potential Estimates in Orlicz Spaces. Pacific Journal of Mathematics, 133, 381-399.
113. Schechter, M. (1988). Boundary Value Problems for Semiliner Elliptic Equations of Arbitrary Order in Unbounded Domains. Rocky Mountain Journal of Mathematics, 18, 519-534.
112. Schechter, M. (1987). Weighted Norm Estimates for Sobolev Spaces. Transactions of the American Mathematical Society, 304, 669-687.
110. Schechter, M. (1987). Two Space Scattering and Propagative Systems. Illinois Journal of Mathematics, 31, 62-88.
109. Schechter, M. (1987). Semilinear Boundary Value Problems for Unbounded Domains. Michigan Mathematical Journal, 34, 63-76.
108. Schechter, M. (1986). Derivatives of Mappings with Applications to Nonlinear Differential Equations. Transactions of the American Mathematical Society, 293, 53-69.
107. Schechter, M. (1984). Differentiation in Abstract Spaces. Journal of Differential Equations, 54, 1-16.
104. Schechter, M. (1984). Self-Adjoint Realizations in Another Hilbert Space. Amer. J. of Math., 106, 43-65.
   
Professional
Society
American Mathematical Society
   
   
Link to this profile http://www.faculty.uci.edu/profile.cfm?faculty_id=2165
   
Last updated 05/30/2011