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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 art́ıculo, probamos la existencia de soluciones homocĺınicas 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 homocĺınicas débiles para datos más generales dependiendo de las soluciones. 2010 AMS Mathematics Subject Classification: 47A75, 35B38, 35P30, 34L05, 34L30. 44 Aboudramane Guiro, Idrissa Ibrango and Stanislas Ouaro CUBO 19, 3 (2017)

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