USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 155-171.

Double resonant problems which are locally non-quadratic at infinity

Marcelo F. Furtado & Elves A. B. Silva

Abstract:
We establish the existence of a nontrivial solution for a double resonant elliptic problem under a local non-quadraticity condition at infinity and pointwise limits. We also study the existence of a nonzero solution when there is resonance at the first eigenvalue. The first result is obtained as an application of an abstract theorem that establishes the existence of a nontrivial critical point for functionals of class C2 on real Hilbert spaces.

Published January 8, 2001.
Math Subject Classifications: 35J65, 58E05.
Key Words: Resonance, non-quadratic at infinity, Morse index.

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Marcelo F. Furtado
Dpto. Matematica
Universidade de Brasilia
70910 Brasilia, DF Brazil
e-mail: furtado@mat.unb.br
Elves A. B. Silva
Dpto. Matematica
Universidade de Brasilia
70910 Brasilia, DF Brazil
e-mail: elves@mat.unb.br

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