Generalized fountain theorem and application to strongly indefinite semilinear problems
Cyril J. Batkam, Fabrice Colin
TL;DR
This paper extends the Fountain Theorem to strongly indefinite functionals using degree theory and applies it to prove the existence of infinitely many solutions for certain semilinear problems, including the Schrödinger equation.
Contribution
It introduces a generalized Fountain Theorem for strongly indefinite functionals and demonstrates its application to semilinear Schrödinger equations.
Findings
Established a version of the Fountain Theorem for strongly indefinite functionals
Proved the existence of infinitely many solutions for specific semilinear problems
Applied the abstract result to the Schrödinger equation
Abstract
By using the degree theory and the 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 Schr\"{o}dinger equation.
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