EXISTENCE OF SOLUTIONS TO THE NON-SELF-ADJOINT STURM-LIOUVILLE PROBLEM WITH DISCONTINUOUS NONLINEARITY

The problem of existence of solutions of the Sturm-Liouville problem with a non-self-adjoint differential operator and non-linearity discontinuous in the phase variable is considered. Theorems on the existence of non-trivial (positive and negative) solutions for positive values of the spectral parameter are established for the problem under study. Examples illustrating the obtained theorems are given.