The Existence Of Solutions To A Class Of Nonlinear Volterra-Stieltjes Integral Equations

Differential equations and integral equations in abstract sp aces,including the existence of solutions of integral-differential equations and its application in Multi-point Boundary Value Problems have become a very active research area in recent years.With the theory and methods of functional analysis,it provides a powerful tool for the research of the existence of solutions of nonlinear problems in Chemistry,Physics,Biology and other subjects.The Lebesgue integral in vector valued functions plays an important role in Vector Valued Measures and the convergence of set-valued measures.The vector valued and set-valued stochastic processes cannot but involve the Riemann-Stieltjes integral(the real values)and its corresponding integral equations.So it has high application value.This paper,from the nonlinear functional analysis theory,by using the fixed point theorem of the measure of noncompactness and convex-power condensing operator,mainly studies on the existence of the solutions of the following nonlinear Volterra-Stieltjes integral equation:(?).With nonlinear integral and relative integral arithmetic operators in nonlinear terms,the conclusion of this paper will enrich the present documents.