On a scaled abstract linking theorem with an application to the Schr\"{o}dinger--Poisson--Slater equation

TL;DR

This paper introduces a generalized linking theorem applicable to variational elliptic equations, notably including Schr"{o}dinger--Poisson--Slater equations, facilitating the proof of existence of solutions.

Contribution

The paper presents a new abstract linking theorem tailored for variational elliptic equations, expanding the toolkit for analyzing complex nonlinear PDEs.

Findings

Proves an abstract linking theorem for elliptic equations

Demonstrates applicability to Schr"{o}dinger--Poisson--Slater equations

Establishes existence results for solutions to these equations

Abstract

We prove an abstract linking theorem that can be used to show existence of solutions to various types of variational elliptic equations, including Schr\"{o}dinger--Poisson--Slater type equations.