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

الملخص EN

We study a new family of measures of noncompactness in the locally Sobolev space Wlocn,1(R+N), 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.