A Family of Measures of Noncompactness in the Locally Sobolev Spaces and Its Applications to Some Nonlinear Volterra Integrodifferential Equations

Abstract

We study a new family of measures of noncompactness in the locally Sobolev space ,1 loc (R + ), equipped with a suitable topology. As an application of the technique associated with this family of measures of noncompactness, we study the existence of solutions for a class of nonlinear Volterra integrodifferential equations. Further, we give an illustrative example to verify the effectiveness and applicability of our results.