Nonlinear elliptic fourth order equations existence and multiplicity results

TL;DR

This paper investigates the existence and multiplicity of solutions for a class of nonlinear fourth order elliptic equations using critical point theory, demonstrating the existence of three solutions in the constant coefficient case.

Contribution

It introduces a novel application of critical point theory to fourth order nonlinear elliptic equations and establishes the existence of multiple solutions for constant coefficient cases.

Findings

Existence of solutions established for the class of equations.

Three distinct solutions found in the constant coefficient case.

Solutions characterized as critical points of a restricted functional.

Abstract

This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a suitable manifold.In the case of constant coefficients we obtain the existence of tree distinct solutions.