Entire large solutions for a class of Schrödinger systems with a nonlinear random operator

Abstract In this paper, we study the nonexistence and existence of radial large positive solutions for a class of Schrodinger systems with a nonlinear random operator under certain growth conditions. We also establish the necessary and sufficient conditions for the existence of radial large positive solutions by a successive iteration technique. The results of the paper improve and extend many previous work in this field of research.

[1]  Alan V. Lair,et al.  A Necessary and Sufficient Condition for the Existence of Large Solutions to Sublinear Elliptic Systems , 2010 .

[3]  Yancong Xu,et al.  A necessary and sufficient condition for the existence of large solutions for (p1, ..., pd)-Laplacian Schrödinger systems with a convection term , 2013, Appl. Math. Lett..

[4]  Yongli Song,et al.  Existence of entire large positive solutions of a semilinear elliptic system , 2004, Appl. Math. Comput..

[5]  Alan V. Lair,et al.  Existence of Entire Large Positive Solutions of Semilinear Elliptic Systems , 2000 .

[6]  Tomomitsu Teramoto.  On nonnegative radial entire solutions of second order quasilinear elliptic systems , 2002 .

[7]  Alan V. Lair,et al.  Entire large solutions to semilinear elliptic systems , 2011 .

[8]  Xinguang Zhang,et al.  The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term , 2010 .

[9]  Dragos-Patru Covei,et al.  Radial and nonradial solutions for a semilinear elliptic system of Schr , 2011, 1105.2652.

[10]  Yahong Peng,et al.  Large solution of a semilinear elliptic problem , 2005 .

[11]  Vicenţiu D. Rădulescu,et al.  Entire solutions blowing up at infinity for semilinear elliptic systems , 2002 .

[12]  Dragos-Patru Covei,et al.  Large and entire large solution for a quasilinear problem , 2009 .

[13]  M. Massar,et al.  Blow-up solutions to a (p, q)-Laplacian system with gradient term , 2012, Appl. Math. Lett..

[14]  Alan V. Lair,et al.  Large solutions of sublinear elliptic equations , 2000 .

[15]  Xinguang Zhang,et al.  A necessary and sufficient condition for the existence of large solutions to 'mixed' type elliptic systems , 2012, Appl. Math. Lett..

[16]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .