Existence of solutions for a problem of resonance road space with weight

TL;DR

This paper extends previous results on the existence of solutions for a nonlinear elliptic problem with resonance and weight from bounded domains to the entire space set^n, using variational methods.

Contribution

It generalizes earlier work by considering unbounded domains set^n, demonstrating the existence of weak solutions in this broader setting.

Findings

Existence of weak solutions in set^n

Extension of previous bounded domain results

Application of variational methods to unbounded domains

Abstract

In this work we use variational methods to show the existence of weak solutions for a nonlinear problem of the type elliptic. This problem was initially study by the authors Ahmad, Lazer and Paul (see \cite{ALP}) considering the space $\Omega\subset\Rset^n$ a bounded domains. In this work we extend your result now considering the domain $\Rset^n$. Indeed, the main theorems in this paper constitute an extension to $\Rset^n$ of your previous results in bounded domains.