Weak homoclinic solutions to discrete nonlinear problems of Kirchhoff type with variable exponents

Guiro, Aboudramane; Ibrango, Idrissa; Ouaro, Stanislas; Guiro, Aboudramane; Ibrango, Idrissa; Ouaro, Stanislas

doi:10.4067/S0719-06462017000300043

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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.19 no.3 Temuco Dec. 2017

http://dx.doi.org/10.4067/S0719-06462017000300043

Articles

Weak homoclinic solutions to discrete nonlinear problems of Kirchhoff type with variable exponents

Aboudramane Guiro¹

Idrissa Ibrango²

Stanislas Ouaro³

^¹Laboratoire de Mathématiques et Informatique (LAMI) UFR. Sciences et Techniques, Universit Nazi BONI 01 BP 1091 Bobo-Dioulasso, 01 Bobo Dioulasso, Burkina Faso. E-mail: abouguiro@yahoo.fr

^²Laboratoire de Mathématiques et Informatique (LAMI) UFR. Sciences et Techniques, Universit Nazi BONI 01 BP 1091 Bobo-Dioulasso, 01 Bobo Dioulasso, Burkina Faso. E-mail: ibrango2006@yahoo.fr

^³Laboratoire de Mathématiques et Informatique (LAMI) UFR. Sciences Exactes et Appliquées Université de Ouagadougou, 03 BP 7021 Ouaga 03 Ouagadougou, Burkina Faso. E-mail: ouaro@yahoo.fr

Abstract

In this paper, we prove the existence of weak homoclinic solutions for discrete nonlinear problems of Kirchhoff type. The proof of the main result is based on a minimization method. As extension, we prove the existence result of weak homoclinic solutions for more general data depending on the solutions.

Resumen

En este artículo, probamos la existencia de soluciones homoclínicas débiles para problemas discretos no-lineales de tipo Kirchhoff. La demostración del resultado principal está basado en un método de minimización. Como extensión, probamos la existencia de soluciones homoclínicas débiles para datos más generales dependiendo de las soluciones.

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