# A variational principle for problems with a hint of convexity

## TL;DR

This paper introduces a new variational principle that extends the ability to solve boundary value problems with a variational structure, especially those beyond traditional compactness constraints, including super-critical elliptic problems.

## Contribution

The paper presents a novel variational principle that broadens the scope of solvable boundary value problems beyond weakly compact structures, addressing super-critical elliptic cases.

## Key findings

- Successfully applied to super-critical semilinear elliptic problems
- Provides a new framework for boundary value problems with non-compact variational structures
- Extends the class of problems solvable via variational methods

## Abstract

A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As a result, we study several super-critical semilinear Elliptic problems.