A class of BVPS for first order impulsive functional integro-differential equations with a parameter

This paper is concerned with a class of boundary value problems for the nonlinear impulsive functional integro-differential equations with a parameter by establishing new comparison principles and using the method of upper and lower solutions together with monotone iterative technique. Sufficient conditions are established for the existence of extremal system of solutions for the given problem. Finally, we give an example that illustrates our results

Integral boundary value problems for first order integro-differential equations with impulsive integral conditions

AbstractThis paper is concerned with the integral boundary value problems for first order integro-differential equations with impulsive integral conditions. Sufficient conditions are obtained for the existence of extremal solutions

On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions (integro-sum inequalities; impulse integral inequalities). Some applications of the results are included: conditions of boundedness (uniformly), stability by Lyapunov (uniformly), practical stability by Chetaev (uniformly) for the solutions of impulsive differential and integro-differential systems of ordinary differential equations

Multiple Positive Solutions of the Singular Boundary Value Problem for Second-Order Impulsive Differential Equations on the Half-Line

This paper uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive singular differential equations on the half-line. The conditions for the existence of multiple positive solutions are established.This work is supported by the National Nature Science Foundation of P. R.China 10871063 and Scientific Research Fund of Hunan Provincial Education Department 07A038 , partially supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, project no.PGIDIT06PXIB207023PRS