We study the solvability of a nonlinear quadratic integral equation of Hammerstein type. Using the technique of measures of noncompactness we prove that this equation has solutions on an unbounded interval. Moreover, we also obtain an asymptotic characterization of these solutions. Several special cases of this integral equation are discussed and applications to real world problems are indicate...

In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

The purpose of this study is to use resolvent operators investigate the existence and controllability a mild solution second-order semilinear integro-differential problem. To construct our criterion, we fixed point theorem in conjunction with measures noncompactness. A practical example used illustrate obtained results.

This paper deals with the existence of solutions for Riemann-Liouville fractional order boundary value problem infinite-point conditions posed on half-line via concept a family measures noncompactness in space functions C?,?(R+) satisfying H?lder condition and generalized Darbo fixed point theorem.