Existence Solutions of Quasilinear Integrodifferential Equations.

      Аннотация: The existence of solutions of quasilinear integrodifferential equations in Banach spaces. Several sufficient conditions are established for the existence of solutions of quasilinear delay integrodifferential equations with nonlocal conditions. Also the existence of mild solutions of quasilinear integrodifferential equations with impulsive conditions is discussed using the Banach contraction principle. Further, we prove the existence results for impulsive quasilinear integrodifferential equations with nonlocal conditions using C0-semigroup and the Schauder fixed point theorem. The same problem is studied by using the analytic semigroup. We also study the existence results for quasilinear impulsive integrodifferential equations by using the Hausdorff measure of noncompactness and the Darbo-Sadovskii fixed point theorem. Finally, we proved the existence results of quasilinear fractional integrodifferential equations. All the results are generalize the previous results of several researchers. Examples are provided to illustrate the theory.

Ключевые слова: analytic semigroup, Banach fixed point theorem, semigroup theory, mild and classical solution, contraction principle, impulsive conditions, Quasilinear integrodifferential equation