Existence of Solution for an Elliptic Problem with a Sublinear Term

TL;DR

This paper proves the existence of positive solutions for elliptic equations with sublinear terms using Galerkin approximations on bounded domains.

Contribution

It establishes the existence of solutions for a class of elliptic problems with sublinear nonlinearities, expanding theoretical understanding.

Findings

Existence of classical positive solutions proven.

Galilean approximation method successfully applied.

Results applicable to bounded domains in RN.

Abstract

In this work we prove the existence of a classical positive solution for an elliptic equation with a sublinear term. We use Galerkin approximations to show existence of such solution on bounded domains in RN.