Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term

2013 ◽  
Vol 219 (10) ◽  
pp. 5345-5355 ◽  
Author(s):  
Indira Mishra ◽  
D. Bahuguna
Keyword(s):  
Differential Equation ◽  
Integro Differential Equation ◽  
Forcing Term ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Automorphic Solution

scholarly journals Weighted Pseudo Almost Automorphic Solutions to Nonautonomous Semilinear Differential Equations

2017 ◽  
Vol 1 (1) ◽  
pp. 27-32
Author(s):  
Saud M. Alsulami
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Evolution Family ◽  
Almost Automorphic ◽  
Exponentially Stable ◽  
Semilinear Differential Equation ◽  
Pseudo Almost Automorphic

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

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