J. Nonl. Evol. Equ. Appl. 2011 no. 7, pp. 101-109, published Oct. 31, 2011:

Almost Periodic Solutions for Hyperbolic Semilinear Evolution Equations

Md. Maqbul and D. Bahuguna

Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur - 208016, India

Received June 22, 2011
Accepted October 10, 2011

Communicated by Michael Ruzhansky

Abstract.  In this paper we study the existence of almost periodic solutions for the semilinear evolution equation du/dt = A u + f(.,u), tR, under the sectoriallity of A, a linear operator with not necessarily dense domain, in a Banach space X and σ(A) ∩ iR=∅ We use the contraction mapping principle to show the existence and uniqueness of an almost periodic solution in an intermediate space Xα, when the function f: R × XαX is Stepanov-almost periodic.
Keywords: Sectorial operator; analytic semigroup; hyperbolic semigroup; Stepanov-almost periodic; almost periodic.
2010 Mathematics Subject Classification:   34G20, 47D06, 34C27, 34K14.

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