Morse theory applied to semilinear problems

References

• Chang , KC . 1993 . Infinite-dimensional Morse Theory and Multiple Solution Problems, Progress in Nonlinear Differential Equations and Their Applications , Vol. 6 , Boston , MA : Birkhäuser Boston Inc. .
   Google Scholar
• Mawhin , J and Willem , M . 1989 . Critical Point Theory and Hamiltonian Systems , New York, Berlin : Springer-Verlag .
   Google Scholar
• Bartsch , T and Li , SJ . 1997 . Critical point theory for asymptotically quadratic functionals and applications to problems with resonance . Nonlinear Anal. , 28 : 419 – 441 .
   Google Scholar
• Liu , JQ . 1989 . The Morse index of a saddle point . Syst. Sci. Math. Sci. , 2 : 32 – 39 .
   Google Scholar
• Schechter , M . 1999 . Linking Methods in Critical Point Theory , Boston : Birkhäuser .
   Google Scholar
• Amann , H and Zehnder , E . 1980 . Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations . Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , 7 ( 4 ) : 539 – 603 .
   Google Scholar
• Costa , DG and Silva , EA . 1995 . On a class of resonant problems at higher eigenvalues . Differ. Integral Eqns. , 8 ( 3 ) : 663 – 671 .
   Google Scholar
• Hirano , N and Nishimura , T . 1993 . Multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities . J. Math. Anal. Appl. , 180 ( 2 ) : 566 – 586 .
   Google Scholar
• Lazer , AC and Solimini , S . 1988 . Nontrivial solutions of operator equations and Morse indices of critical points of min–max type . Nonlinear Anal. TMA , 12 ( 8 ) : 761 – 775 .
   Google Scholar
• Li , SJ and Liu , JQ . 1992 . Nontrivial critical points for asymptotically quadratic function . J. Math. Anal. Appl. , 165 ( 2 ) : 333 – 345 .
   Google Scholar
• Li , SJ and Liu , JQ . 1999 . Computations of critical groups at degenerate critical point and applications to nonlinear differential equations with resonance . Houston J. Math. , 25 ( 3 ) : 563 – 582 .
   Google Scholar
• Li , S and Willem , M . 1998 . Multiple solutions for asymptotically linear boundary value problems in which the nonlinearity crosses at least one eigenvalue . Nonlinear Diff. Eqns. Appl. , 5 : 479 – 490 .
   Google Scholar
• Li , SJ and Zhang , Z . 1999 . Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity . Discr. Contin. Dynam. Syst. , 5 ( 3 ) : 489 – 493 .
   Google Scholar
• Li , SJ and Zou , W . 1999 . The computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue . J. Math. Anal. Appl. , 235 ( 1 ) : 237 – 259 .
   Google Scholar
• Perera , K . 1999 . Applications of local linking to asymptotically linear elliptic problems at resonance . Nonlinear Diff. Eqns. Appl. , 6 ( 1 ) : 55 – 62 .
   Google Scholar
• Perera , K and Schechter , M . 1998 . Type II regions between curves of the Fučik spectrum and critical groups . Topol. Methods Nonlinear Anal. , 12 ( 2 ) : 227 – 243 .
   Google Scholar
• Perera , K and Schechter , M . 2000 . A generalization of the Amann–Zehnder theorem to nonresonance problems with jumping nonlinearities . Nonlinear Diff. Eqns. Appl. , 7 ( 4 ) : 361 – 367 .
   Google Scholar
• Perera , K and Schechter , M . 2001 . The Fučík spectrum and critical groups . Proc. Amer. Math. Soc. , 129 ( 8 ) : 2301 – 2308 . (electronic)
   Google Scholar
• Schechter , M . 1995 . Bounded resonance problems for semilinear elliptic equations . Nonlinear Anal. TMA , 24 ( 10 ) : 1471 – 1482 .
   Google Scholar
• Silva , EA . 1991 . Linking theorems and applications to semilinear elliptic problems at resonance . Nonlinear Anal. , 16 ( 5 ) : 455 – 477 .
   Google Scholar
• Su , J and Tang , C . 2001 . Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues . Nonlinear Anal. (Ser. A: Theory Methods) , 44 ( 3 ) : 311 – 321 .
   Google Scholar
• Zou , W and Liu , JQ . 2001 . Multiple solutions for resonant elliptic equations via local linking theory and Morse theory . J. Diff. Eqns. , 170 ( 1 ) : 68 – 95 .
   Google Scholar