Existence Theorem for One Class of Strongly Resonance Boundary-Value Problems of Elliptic Type with Discontinuous Nonlinearities

Abstract

We consider the Dirichlet problem for an equation of the elliptic type with a nonlinearity discontinuous with respect to the phase variable in the resonance case; it is not required that the nonlinearity satisfy the Landesman-Lazer condition. Using the regularization of the original equation, we establish the existence of a generalized solution of the problem indicated.