An infinite dimensional saddle point theorem and application

2025/05/07 by Colin, Fabrice, Songo, Ablanvi · 3 citations
#35J10 #35J61 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04809

Abstract

By using the τ-topology of Kryszewski and Szulkin, we establish a natural new version of the Saddle Theorem for strongly indefinite functionals. The abstract result will be applied for studying the existence of a nontrivial solution of the strongly indefinite semilinear Schrödinger equation where the associated functional is indefinite, that is, the functional is of the form J(u) = \dfrac12 ⟨ Lu, u ⟩ - Ψ(u) defined on a Hilbert space X, where L : X → X is a self-adjoint operator with negative and positive eigenspace both infinite-dimensional.

Citations

• On differential systems with strongly indefinite variational structure

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• Existence result for a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities
• On the Fountain Theorem for Continuous Functionals and Its Application to a Semilinear Elliptic Problem in ℝ²
• A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

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