Bifurcation results for semilinear elliptic problems in R^N

TL;DR

This paper investigates bifurcation phenomena for semilinear elliptic equations in ^N, identifying solution families emerging from the spectrum's bottom using variational methods and nonlinear reduction techniques.

Contribution

It introduces a novel application of nonlinear reduction to find bifurcating solutions in semilinear elliptic problems in ^N.

Findings

Families of solutions bifurcating from the spectrum's bottom identified

Application of variational and nonlinear reduction methods demonstrated

Solution structures characterized near the spectrum's bottom

Abstract

In this paper we obtain, for a semilinear elliptic problem in R^N, families of solutions bifurcating from the bottom of the spectrum of $-\Delta$. The problem is variational in nature and we apply a nonlinear reduction method which allows us to search for solutions as critical points of suitable functionals defined on finite-dimensional manifolds.