Multiple solutions for elliptic equations involving a general operator in divergence form

TL;DR

This paper uses variational methods to establish the existence of three weak solutions for a broad class of elliptic equations involving divergence form operators, including specific cases and an application example.

Contribution

It introduces a novel approach to prove multiple solutions for elliptic equations with general divergence form operators, extending previous results.

Findings

Existence of three weak solutions for the studied elliptic equations

Application to a specific uniformly elliptic second-order problem

Analysis of special cases within the general framework

Abstract

In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special cases are analyzed. In conclusion, for completeness, a concrete example of an application is presented by finding the existence of three nontrivial weak solutions for an uniformly elliptic second-order problem on a bounded Euclidean domain.