Open AccessWeighted Pseudo Almost Automorphic Solutions to Nonautonomous Semilinear Differential Equations
Author(s) -
Saud M. Alsulami
Publication year - 2017
Publication title -
journal of mathematical sciences and computer applications
Language(s) - English
Resource type - Journals
ISSN - 2158-933X
DOI - 10.5147/jmsca.v1i1.88
Subject(s) - lipschitz continuity , mathematics , uniqueness , banach space , exponential dichotomy , pure mathematics , space (punctuation) , argument (complex analysis) , differential equation , mathematical analysis , linguistics , biochemistry , chemistry , philosophy
We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutionsto the non-autonomous semilinear differential equation in a Banach space X :( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t Rwhere A(t), t R, generates an exponentially stable evolution family {U(t, s)} andf :R X X satisfies a Lipschitz condition with respect to the second argument.MSC 2010: 43A60; 34G20, 47Dxx