The Computations of the Critical Groups with an Application to Elliptic Resonant Problems at a Higher Eigenvalue

Abstract

In this paper, we study the existence of a nontrivial solution of the elliptic problem which is a resonant type both at the origin and at infinity with the same higher eigenvalue, and the nonlinear term is permitted to be unbounded. Our main ingredient is the computation of the critical groups. © 1999 Academic Press.