Existence results for a class of quasilinear integrodifferential equations of Volterra–Hammerstein type with nonlinear boundary conditions

Abstract

Abstract. The existence of a solution for a class of quasilinear integrodifferential equations of Volterra-Hammerstein type with nonlinear boundary conditions is established. Such equations occur in the study of the p-Laplace equation, generalized reactiondiffusion theory, non-Newtonian fluid theory, and in the study of turbulent flows of a gas in a porous medium. The results are obtained by using upper and lower solutions, and extend some previously known results.In this paper we study existence results for the integrodifferential equationsubject to one of the following boundary conditions:, where