On a number of solutions in problems with spectral parameter for equations with discontinuous operators

Abstract

In a real reflexive Banach space we consider a problem on existence of solutions to a problem with a spectral parameter for equations with discontinuous operators. By the variational approach we obtain theorems on the number of the solutions to the considered problems. As an application, we consider main boundary value problems for elliptic equations with a spectral parameter and discontinuous nonlinearities.