Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

In recent years, the theory of almost automorphic functions has been developed extensively see, e.g., Bugajewski and N’guérékata 1 , Cuevas and Lizama 2 , and N’guérékata 3 and the references therein . However, literature concerning pseudo-almost automorphic functions is very new cf. 4 . It is well known that the study of composition of two functions with special properties is important and bas...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

Weighted Pseudo Almost Automorphic Solutions to Non- autonomous Semilinear Differential Equations

We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutions to the non-autonomous semilinear differential equation in a Banach space X : ( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t R where ( ), , A t t R generates an exponentially stable evolution family { ( , )} U t s and : f X X R satisfies a Lipschitz condition with respect to the second argument. MSC 2010: 4...

Almost automorphic solutions to some classes of partial evolution equations

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. c © 2006 Elsevier Ltd. All rights reserved.

Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations

By applying the Horn’s fixed point theorem, we prove the existence of T0-periodic PC-mild solution of impulsive periodic systems when PC-mild solutions are ultimate bounded.