Weak solutions to Neumann discrete nonlinear system of Kirchhoff type

• Autores: Rodrigue Sanou, Idrissa Ibrango, Blaise Koné, Aboudramane Guiro
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 21, Nº. 3, 2019, págs. 75-91
• Idioma: inglés
• DOI: 10.4067/S0719-06462019000300075
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Probamos la existencia de soluciones débiles para sistemas discretos no-lineales de tipo Kirchhoff. Construimos algunos espacios de Hilbert con normas apropiadas. Definimos la noción de solución débil correspondiente al problema (1.1). La demostración del resultado principal se basa en un método de minimización de un funcional de energía J.

  • English

    Abstract We prove the existence of weak solutions for discrete nonlinear system of Kirchhoff type. We build some Hilbert spaces with suitable norms. We define the notion of weak solution corresponding to the problem (1.1). The proof of the main result is based ona minimization method of an energy functional J.

• Referencias bibliográficas
  • Bonanno, G.,Molica Bisci, G.,Radulescu, V.. (2012). Arbitrarity small weak solutions for nonlinear eigenvalue problem in Orlicz-Sobolev spaces,....
  • Cai, X.,Yu, J.. (2006). Existence theorems for second-order discrete boundary value problems. J. Math. Anal. Appl.. 320. 649
  • Castro, A.,Shivaji, R.. (1989). Nonnegative solutions for a class of radically symmetric nonpositone problems. Proceedings of the American...
  • Chen, Y.,Levine, S.,Rao, M.. (2006). Variable exponent, linear growth functionals in image restoration. SIAM Journal on Applied Mathematics....
  • Diening, L.. (2002). Theoretical and numerical results for electrorheogica fluids. University of Freiburg.
  • Guiro, A.,Nyanquini, I.,Ouaro, S.. (2011). On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian. Adv. Differ....
  • Koné, B.,Ouaro, S.. (2010). Weak solutions for anisotropic discrete boundary value problems. J. Differ. Equ. Appl.. 16. 1-11
  • Mihailescu, M.,Radulescu, V.,Tersian, S.. (2009). Eigenvalue problems for anisotropic discrete boundary value problems. J. Differ. Equ. Appl.....
  • Rajagopal, K. R.,Ruzicka, M.. (2001). Mathematical modeling of electrorheological materials. Continuum Mechanics and Thermodynamics. 13. 59-78
  • Ruzicka, M.. (2000). Modeling and Mathematical Theory. Springer. Berlin, Germany.
  • Yucedag, Z.. (2014). Existence of solutions for anisotropic discrete boundary value problems of Kirch-hoff type. Int. J. Differ. Equ. Appl....
  • Zhang, G.,Liu, S.. (2007). On a class of semipositone discrete boundary value problem. J. Math.Anal. Appl.. 325. 175
  • Zhao, J.. (2018). Positive solutions and eigenvalue intervals for a second order p-Laplacian discrete system. Adv. Differ. equ.. 2018.
  • Zhikov, V.. (1987). Averaging of functionals in the calculus of variations and elasticity. Mathematics of the USSR-Izvestiya. 29. 33-66