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The Fucik spectrum and critical groups


Authors: Kanishka Perera and Martin Schechter
Journal: Proc. Amer. Math. Soc. 129 (2001), 2301-2308
MSC (2000): Primary 35J65, 58E05, 49B27
Published electronically: February 2, 2001
MathSciNet review: 1823913
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Abstract | References | Similar Articles | Additional Information

Abstract:

We compute critical groups of zero for variational functionals arising from semilinear elliptic boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in certain parts of Type (II) regions between curves of the Fucik spectrum.


References [Enhancements On Off] (What's this?)

  • 1. E. N. Dancer, Multiple solutions of asymptotically homogeneous problems, Ann. Mat. Pura Appl. (4) 152 (1988), 63–78. MR 980972, 10.1007/BF01766141
  • 2. E. N. Dancer.
    Remarks on jumping nonlinearities.
    In Topics in nonlinear analysis, pages 101-116. Birkhäuser, Basel, 1999. CMP 2000:05
  • 3. Thierry Gallouët and Otared Kavian, Résultats d’existence et de non-existence pour certains problèmes demi-linéaires à l’infini, Ann. Fac. Sci. Toulouse Math. (5) 3 (1981), no. 3-4, 201–246 (1982) (French, with English summary). MR 658734
  • 4. K. Perera and M. Schechter.
    A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities.
    to appear in NoDEA Nonlinear Differential Equations Appl. 7 (2000) no. 3.
  • 5. Kanishka Perera and Martin Schechter, Type II regions between curves of the Fučik spectrum and critical groups, Topol. Methods Nonlinear Anal. 12 (1998), no. 2, 227–243. MR 1701261
  • 6. M. Schechter.
    Resonance problems with respect to the Fucík spectrum.
    Trans. Amer. Math. Soc., 352:4195-4205, 2000. CMP 2000:14
  • 7. Martin Schechter, The Fučík spectrum, Indiana Univ. Math. J. 43 (1994), no. 4, 1139–1157. MR 1322614, 10.1512/iumj.1994.43.43050
  • 8. Martin Schechter, Type (II) regions between curves of the Fucik spectrum, NoDEA Nonlinear Differential Equations Appl. 4 (1997), no. 4, 459–476. MR 1485732, 10.1007/s000300050025

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Additional Information

Kanishka Perera
Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901-6975
Email: kperera@winnie.fit.edu

Martin Schechter
Affiliation: Department of Mathematics, University of California–Irvine, Irvine, California 92697-3875
Email: mschecht@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05968-8
Received by editor(s): November 26, 1999
Published electronically: February 2, 2001
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2001 American Mathematical Society