On nonlinear integro-differential equations of hyperbolic type

摘要

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 minimalmaximal solutions may be constructed from a single pair of coupled lowerupper solutions. The coupled minimalmaximal solutions coincide in a unique solution provided the problem satisfies certain one-sided Lipschitz conditions.