Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 3, Number 3-4 (1998), 425-436.
Almost periodic mild solutions of a class of partial functional differential equations
We study the existence of almost periodic mild solutions of a class of partial functional differential equations via semilinear almost periodic abstract functional differential equations of the form To this end, we first associate with every almost periodic semilinear equation a nonlinear semigroup in the space of almost periodic functions. We then give sufficient conditions (in terms of the accretiveness of the generator of this semigroup) for the existence of almost periodic mild solutions of (**) as fixed points of the semigroup. Those results are then carried over to equation (*). The main results are stated under accretiveness conditions of the function in terms of and Lipschitz conditions with respect to .
Abstr. Appl. Anal., Volume 3, Number 3-4 (1998), 425-436.
First available in Project Euclid: 8 April 2003
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35R10: Partial functional-differential equations 35B15: Almost and pseudo-almost periodic solutions
Secondary: 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]
Aulbach, Bernd; Minh, Nguyen Van. Almost periodic mild solutions of a class of partial functional differential equations. Abstr. Appl. Anal. 3 (1998), no. 3-4, 425--436. doi:10.1155/S1085337598000645. https://projecteuclid.org/euclid.aaa/1049832735