ELLIPTIC PROBLEM WITH A VARIABLE COEFFICIENT AND A JUMPING SEMILINEAR TERM

Abstract

We obtain the multiple solutions for the fourth order
elliptic problem with a variable coefficient and a jumping semilinear
term. We have a result that there exist at least two solutions if the
variable coefficient of the semilinear term crosses some number of the
eigenvalues of the biharmonic eigenvalue problem. We obtain this
multiplicity result by applying the Leray-Schauder degree theory.