Positive solutions for asymptotically linear problems in exterior domains

TL;DR

This paper proves the existence of positive solutions for certain asymptotically linear differential problems in exterior domains using advanced variational methods.

Contribution

It introduces a novel approach combining linking arguments on the Nehari manifold with barycenter functions for exterior domain problems.

Findings

Positive solutions are established for the class of problems considered.

The method extends variational techniques to exterior domain asymptotically linear problems.

The approach provides a framework for future research in similar nonlinear differential equations.

Abstract

The existence of a positive solution for a class of asymptotically lin- ear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter function.