Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides

Abstract

The question on the existence of solutions to eigenvalue problems is treated for nonlinear equations with discontinuous operators in a real Hilbert space. Using a variational method, theorems on the existence of two nontrivial solutions for sufficiently large values of the spectral parameter are proved. As an application, eigenvalue problems for elliptic-type equations with nonlinear terms which are discontinuous in the phase variable are investigated. Bibliography: 22 titles.