On number of solutions in eigenvalue problems for elliptic equations with discontinuous nonlinearities

Abstract

We study the existence of solutions of eigenvalue problems for elliptic equations of the second order with nonlinearity discontinuous with respect to a phase variable. Using the variational method, we receive the theorems on number of solutions for investigated problems. M. A. Goldshtiks problem on separated flows of incompressible fluid is considered as an appendix.

Keywords

• boundary value problems
• elliptic equations
• eigenvalue problems
• discontinuous nonlinearity
• variational method
• number of solutions