Existence and concentration of solutions for a class of biharmonic equations

TL;DR

This paper investigates superlinear fourth-order elliptic equations, establishing the existence of ground state solutions that concentrate at a point, using variational methods and truncated equations.

Contribution

It proves the existence and concentration of solutions for a class of biharmonic equations, advancing understanding of their solution behavior.

Findings

Ground states exist for the considered equations.

Solutions concentrate at a point in the limit.

Variational methods are effective for these problems.

Abstract

Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial solutions are related to a suitable truncated equation.