EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN

Abstract

We consider the multiplicity of the solutions for the
elliptic boundary value problem with $C^1$ nonlinear term decaying
at the origin. We get a theorem which shows the existence of the
nontrivial solution for the elliptic problem with $C^1$ nonlinear term
decaying at the origin. We obtain this result by reducing the el-
liptic problem with the $C^1$ nonlinear term to the elliptic problem
with bounded nonlinear term and then approaching the variational
method and using the mountain pass geometry for the reduced the
elliptic problem with bounded nonlinear term.