Generalized fountain theorem and application to strongly indefinite semilinear problems

Abstract

By using the degree theory and the $\tau -$topology of Kryszewski and Szulkin, we establish a version of the Fountain Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of infinitely many solutions of two strongly indefinite semilinear problems including the semilinear Schrödinger equation.

References in corpus (1)

• Periodic nonlinear Schrödinger equation with application to photonic crystals

Cited by in corpus (7)

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• Radial and nonradial solutions of a strongly indefinite elliptic system on ${\mathbb{R}}^N$
• An infinite dimensional saddle point theorem and application
• Infinitely many small energy solutions of a semilinear Schrodinger equation
• Infinitely many solutions for a Schrodinger equation with sign-changing potential and nonlinear term
• Nontrivial solutions for periodic Schrödinger equations with sign-changing nonlinearities
• On differential systems with strongly indefinite variational structure