Monotone Method For Single And Multivalued Differential Inequalities With Applications

Abstract

In this paper, the existence of the extremal solutions of first order single and multi-valued nonlinear differential equations, with discontinuous right hand side is proved, via monotone method together with the applications of lattice fixed point technique of Tarski. Two basic single and multi-valued differential inequalities are obtained which are further applied for proving the boundendness and uniqueness of the solution, of the related single and multi-valued differential equations.