Short Communications ON THE EXISTENCE OF BOUNDED SOLUTIONS FOR SYSTEMS OF NONLINEAR GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS

Abstract. Sufficient conditions are given for the existence of bounded solutions for the systems of nonlinear generalized ordinary differential equations. 2000 Mathematics Subject Classification: 34K10. Key words and phrases: Systems of nonlinear generalized ordinary differential equations, the Lebesgue-Stiltjes integral, existence of bounded solutions, sufficient conditions. n → R n be a vector-function belonging to the Carathéodory class corresponding to the matrix-function A. In this paper we investigate the question of existence of solutions for the system of generalized ordinary differential equations , satisfying one of the following two conditions We give sufficient conditions for the existence of solutions of the boundary value problems (1)