On nonlinear integro-differential equations of hyperbolic type

Abstract

This paper considers unified initial-boundary value problems for integro-differential equations of hyperbolic type. For such problems where the forcing functions satisfy certain monotonicity conditions, monotone sequences converging to coupled minimal–maximal solutions may be constructed from a single pair of coupled lower–upper solutions. The coupled minimal–maximal solutions coincide in a unique solution provided the problem satisfies certain one-sided Lipschitz conditions.