Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space - Applied Mathematics

AM > Vol.7 No.15, September 2016

Volume 7, Issue 15 (September 2016)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space ()

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DOI: 10.4236/am.2016.715145 1,673 Downloads 2,457 Views Citations

Author(s)

William Dimbour¹, Vincent Valmorin²

Affiliation(s)

¹UMR Espace-Dev Université de Guyane, Cayenne, Guyane.
²Laboratoire C.E.R.E.G.M.I.A. Université des Antilles, Pointe-à-Pitre, Guadeloupe.

ABSTRACT

In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory.

KEYWORDS

Asymptotically ω-Antiperiodic Functions, Differential Equations with Piecewise Constant Argument, Semi-Group

Share and Cite:

Dimbour, W. and Valmorin, V. (2016) Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space. Applied Mathematics, 7, 1726-1733. doi: 10.4236/am.2016.715145.

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