zbMATH — the first resource for mathematics

Stepanov-like almost automorphic functions and applications to some semilinear equations. (English) Zbl 1128.43006
The abstract semilinear parabolic differential equation \(u'(t)=Au(t)+ F(x,u(t))\), where \(A:D(A)\subset X\to X\) is an infinitesimal generator of an exponentially stable \(G_\delta\)-semigroup on a Banach space \(X\) and \(F:R\times X\to X\) is \(S^p\)-almost automorphic for \(p>1\) and jointly continuous, is considered. The concept of Stepanov-like almost automorphy, introduced by N’Guérékata and Paskov, is used for the proof of the conditions for the existence and uniqueness of the almost automorphic solution of this equation.

43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
34G20 Nonlinear differential equations in abstract spaces
Full Text: DOI
[1] DOI: 10.1073/pnas.52.4.907 · Zbl 0134.30102 · doi:10.1073/pnas.52.4.907
[2] Bugajewski D, Nonlinear Studies 13 pp 129– (2006)
[3] DOI: 10.1090/S0002-9939-04-07571-9 · Zbl 1053.34050 · doi:10.1090/S0002-9939-04-07571-9
[4] Gal CS, Forum Mathematicum 71 pp 201– (2005)
[5] DOI: 10.1090/S0002-9939-05-07790-7 · Zbl 1073.34073 · doi:10.1090/S0002-9939-05-07790-7
[6] N’Guérékata GM, Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces (2001)
[7] DOI: 10.1007/s00233-003-0021-0 · Zbl 1077.47058 · doi:10.1007/s00233-003-0021-0
[8] N’Guérékata GM, Topics in Almost Automorphy (2005) · Zbl 1073.43004
[9] N’Guérékata GM, Far East Journal of Mathematical Sciences (FJMS) 17 pp 337– (2005)
[10] N’Guérékata GM, Nonlinear Analysis
[11] Pankov A, Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations (1990) · Zbl 0712.34001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.