A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

2025/06/21 by Songo, Ablanvi, Colin, Fabrice · 2 citations
#35J05 #35J61 #35J91 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17563

Abstract

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value c of a functional f can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the τ-topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]Wi. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations.

Citations

• An infinite dimensional saddle point theorem and application
• On differential systems with strongly indefinite variational structure

Cited by

• 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

Related

• On the Linking Principle
• An abstract linking theorem applied to indefinite problems via spectral\n properties
• On a scaled abstract linking theorem with an application to the Schrödinger--Poisson--Slater equation
• Linking theorems for multivalued functionals and application to partial differential inclusions
• Infinitely many solutions for Kirchhoff equations with indefinite potential