Convex Solutions of a Nonlinear Integral Equation of Urysohn Type

We study the solvability of a nonlinear integral equation of Urysohn type. Using the technique of measures of noncompactness we prove that under certain assumptions this equation possesses solutions that are convex of order for each , with being a given integer. A concrete application of the results obtained is presented.</p

On the solvability of a nonlinear functional integral equations via measure of noncompactness in

Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions Lp(RN). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result

On a coupled system of functional integral equations of Urysohn type

In this paper we shall study some existence theorems of solutions for a coupled&nbsp;system of functional integral equations of Urysohn type

Equations with discontinuous nonlinear semimonotone operators

summary:The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type $x+KF(x)=0$ with the discontinuous semimonotone operator $F$. Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in $L_p(\Omega )$ are given for illustration