Existence of entire solutions for quasilinear eliptic systems under keller-osserman condition

• Yuan Zhang ^[1] ; Zuodong Yang ^[1]
  1. [1] Nanjing Normal University

     Nanjing Normal University

     China

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 1, 2013, págs. 119-130
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000100008
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo estudiamos la existencia de soluciones enteras para el siguiente sistema elíptico △m u = p(x) f (v), △l v = q (x) g (u), x E R N, donde 1 < m, l <∞, f, g son continuas y no-decrecientes en [0,∞), satisfaciendo f (t) > 0, g(t) > 0 para todo t > 0 y la condición de Keller-Osserman. Establecemos condiciones sobre p y qy que son necesarias para la existencia de soluciones positivas, acotadas y no acotadas de la ecuación dada.

  • English

    In this paper, we study the existence of entire solutions for the following elliptic system △mu = p(x) f (v), △lv = q (x) g (u), x E R N, where 1 < m, l <∞, f, g are continuous and non-decreasing on [0,∞), satisfy f (t) > 0, g(t) > 0 for all t > 0 and the Keller-Osserman condition. We establish conditions on p and q that are necessary for the existence of positive solutions, bounded and unbounded, of the given equation.

• Referencias bibliográficas
  • Cirstea, F,Radulescu, V. D. (2002). Entire solutions blowing up at infinity for semilinear elliptic systems. J. Math. Pures Appl. 81. 827-846
  • Clement, Ph,de Figueiredo, D.G,Mitidieri, E. (1992). Positive solutions of semilinear elliptic systems. Comm. in P.D.E. 56. 923-940
  • Clement, Ph,Manasevich, R,Mitidieri, E. (1993). Positive solutions for a quasilinear system via blow up. Comm. in Partial Diff. Eqns. 12....
  • Felmer, P. L,Manasevich, R,de Thelin, F. (1992). Existence and uniqueness of positive solutions for certain quasilinear elliptic system. Comm.in...
  • García-Melián, J. (2007). A remark on uniqueness of large solutions for elliptic systems of competitive type. J.Math.Anal.Appl. 331. 608-616
  • Ghanmi, A,Mâagli, H,Radulescu, V,Zeddini, N. (2009). Large and bounded solutions for a class of nonlinear Schrödinger stationary systems....
  • Gidas, B,Ni, W.M,Nirenberg, L. (1979). Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68. 209-243
  • Guo, Zongming. (1992). Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems. Nonlinear Anal. 18....
  • Guo, Zongming,Webb, J.R.L. (1994). Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large. Proc.Roy.Soc....
  • Guo, Zongming. (1996). Existence of positive radial solutions for a class of quasilinear elliptic systems in annular domains. Chinese Journal...
  • Kichenassamy, S,Smoller, J. (1990). On the existence of radial solutions of quasilinear elliptic equations. Nonlinearity. 3. 677-694
  • Lair, A. V,Wood, A. W. (2000). Existence of entire large positive solutions of semilinear elliptic systems. J. Differential Eqns. 2. 380-394
  • Mitidieri, E. (1996). Nonexistence of positive solutions of semilinear elliptic system in RN. Diff. Integral Equations. 9. 465-479
  • Mitidieri, E,Rellich, A. (1993). type identity and applications. Comm. in Partial Diff. Equations. 18. 125-171
  • Mitidieri, E,Sweers, G,van der Vorst, R. (1995). Nonexistence theorems for systems of quasilinear partial differential equations. Differential...
  • Peletier, L. A,van der Vorst, R. (1992). Existence and non-existence of positive solutions of non-linear elliptic systems and the biharmonic...
  • Wang, X,Wood, A.W. (2002). Existence and nonexistence of entire positive solutions of semilinear elliptic system. J.Math.Anal.Appl. 267. 361-362
  • Yang, Zuodong. (2004). Existence of positive bounded entire solutions for quasilinear elliptic equation. Applied Mathematics and Computation....
  • Yang, Zuodong. (2003). Existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems. J. Math. Anal...
  • Yang, Zuodong. (2006). Existence of explosive positive solutions of quasilinear elliptic equations. Applied Mathematics and Computation. 177....
  • Yang, Zuodong,Lu, Q. S. (2000). Non-existence of positive radial solutions for a class of quasilinear elliptic system. Comm. Nonlinear Sci....
  • Yang, Zuodong,Lu, Qishao. (2001). Existence of entire explosive positive radial solutions of sublinear elliptic systems. Communication Nonlinear...
  • Zhang, Zhijun,Shi, Yongxiu,Xue, Yanxing. (2011). Existence of entire solutions for semilinear elliptic systems under Keller-Osserman condition....