Pseudo-almost-periodic solutions to some semilinear differential equations

We study the existence and uniqueness of pseudo-almost-periodic solutions to semilinear differential equations of the form (*)u^'(t)+Au(t)=f(t,u(t)), where -A is the infinitesimal generator of an analytic semigroup acting on a (complex) Banach space X, and f:[email protected]?X is a jointly continuous function. Under some additional assumptions on A and f, the existence and uniqueness of a pseudo-almost-periodic (classical) solution to (*) is obtained by using both fractional powers of operators and the Banach's fixed-point principle.

[1]  Gaston M. N’Guérékata,et al.  Almost Automorphic and Almost Periodic Functions in Abstract Spaces , 2001 .

[2]  O. Arino,et al.  Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations , 1996 .

[3]  Gaston M. N'Guérékata,et al.  Topics in Almost Automorphy , 2004 .

[4]  O. Arino,et al.  Pseudo almost periodic solutions for some differential equations in a Banach space , 1997 .

[5]  G. Folland.  Introduction to Partial Differential Equations , 1976 .

[6]  Mohamed Bahaj,et al.  Almost periodic solutions of semilinear equations with analytic semigroups in Banach spaces , 2002 .

[7]  Janusz Traple.  Weak almost periodic solutions of differential equations , 1982 .

[8]  Toka Diagana,et al.  Pseudo almost periodic solutions to some differential equations , 2005 .

[9]  R. Rogers,et al.  An introduction to partial differential equations , 1993 .

[10]  Lahcen Maniar,et al.  Composition of pseudo almost periodic functions and Cauchy problems with operator of non dense domain , 1999 .

[11]  Chuanyi Zhang,et al.  Integration of vector-valued pseudo-almost periodic functions , 1994 .

[12]  Samuel Zaidman,et al.  Topics in Abstract Differential Equations , 1994 .

[13]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[14]  Hong-Xu Li,et al.  Composition of Pseudo Almost-Periodic Functions and Semilinear Differential Equations , 2001 .

[15]  Jerome A. Goldstein.  CONVEXITY, BOUNDEDNESS,ANDALMOST PERIODICITY FOR DIFFERENTIAL EQUATIONS IN HILBERTSPACE , 1979 .

[16]  Alexander Pankov,et al.  Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations , 1990 .

[17]  Claudio Cuevas,et al.  Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain , 2001 .

[18]  Yoshiyuki Hino,et al.  Almost Periodic Solutions of Differential Equations in Banach Spaces , 2001 .

[19]  Chuanyi Zhang.  Pseudo Almost Periodic Solutions of Some Differential Equations, II , 1994 .

[20]  Bashir Ahmad,et al.  Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions , 2002 .

[21]  A. Fink.  Almost Periodic Differential Equations , 1974 .

[22]  Constantin Corduneanu,et al.  Almost periodic functions , 1968 .