Electron. J. Diff. Equ., Vol. 2015 (2015), No. 241, pp. 1-10.

Existence of bounded solutions for nonlinear hyperbolic partial differential equations

Toka Diagana, Mamadou Moustapha Mbaye

Abstract:
In this article we first establish a new representation formula for bounded solutions to a class of nonlinear second-order hyperbolic partial differential equations. Next, we use of our newly-established representation formula to establish the existence of bounded solutions to these nonlinear partial differential equations.

Submitted July 4, 2015. Published September 21, 2015.
Math Subject Classifications: 43A60, 34B05, 34C27, 42A75, 47D06, 35L90.
Key Words: Hyperbolic partial differential equations; bounded solutions; almost automorphic; pseudo-almost automorphic.

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Toka Diagana
Department of Mathematics, Howard University
2441 6th Street N.W., Washington, DC 20059, USA
email: tdiagana@howard.edu
Mamadou Moustapha Mbaye
Université Gaston Berger de Saint-Louis
UFR SAT, Département de Mathématiques, B.P. 234
Saint-Louis, Sénégal
email: tafffmbaye@yahoo.fr

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