Existence of nontrivial solutions for singular quasilinear elliptic equations on RNRN

In this paper, we study the existence of weak solutions for the singular quasilinear elliptic problem (0.1){-div(|x|^-^a^p|@?u|^p^-^2@?u)+V(x)|u|^p^-^2u=h(x)|u|^s^-^2u+/-H(x)|u|^r^-^2u,x@?R^N,u(x)->0,as|x|->~, where 1

[1]  Jin Wook Kim,et al.  Decomposition of Chinese characters into strokes using mathematical morphology , 1999 .

[2]  Three positive solutions for a semilinear elliptic equation in R N involving sign-changing weight , 2011 .

[3]  F. Brock,et al.  EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH WEIGHTS , 2006 .

[4]  P. Rabinowitz,et al.  Dual variational methods in critical point theory and applications , 1973 .

[5]  Jiabao Su,et al.  Weighted Sobolev embedding with unbounded and decaying radial potentials , 2007 .

[6]  W. Ni,et al.  On the existence of positive entire solutions of a semilinear elliptic equation , 1986 .

[7]  Athanasios N. Lyberopoulos.  Quasilinear scalar field equations with competing potentials , 2011 .

[8]  P. C. Carrião,et al.  Subcritical perturbations of a singular quasilinear elliptic equation involving the critical Hardy–Sobolev exponent , 2007 .

[9]  W. Rother,et al.  Nonlinear scalar field equations , 1992, Differential and Integral Equations.

[10]  K. J. Brown,et al.  A fibering map approach to a potential operator equation and its applications , 2009, Differential and Integral Equations.

[11]  Jiabao Su,et al.  Sobolev type embedding and quasilinear elliptic equations with radial potentials , 2011 .

[12]  Vicentiu D. Rădulescu,et al.  Existence and Non-Existence Results for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions , 2007, 0706.2403.

[13]  Benjin Xuan.  The solvability of quasilinear Brezis–Nirenberg-type problems with singular weights , 2005 .

[14]  Vicentiu D. Rădulescu,et al.  Ground state solutions of non‐linear singular Schrödinger equations with lack of compactness , 2003 .

[15]  Vicentiu D. Rădulescu,et al.  Weak solutions of quasilinear problems with nonlinear boundary condition , 2001 .

[16]  J. Lions,et al.  Physical origins and classical methods , 1990 .

[17]  P. Han.  QUASILINEAR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENTS AND HARDY TERMS , 2005 .

[18]  Jacques-Louis Lions,et al.  Mathematical Analysis and Numerical Methods for Science and Technology: Volume 1 Physical Origins and Classical Methods , 1990 .

[19]  Alexander Gladkov,et al.  ENTIRE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS , 2004 .

[20]  Robert V. Kohn,et al.  First order interpolation inequalities with weights , 1984 .

[21]  Singular elliptic problems with lack of compactness , 2005, math/0502096.

[22]  Shujie Li,et al.  On multiple solutions of a singular quasilinear equation on unbounded domain , 2002 .

[23]  Pierre-Louis Lions,et al.  Nonlinear scalar field equations, I existence of a ground state , 1983 .

[24]  L. Yu.  Nonlinear p-Laplacian problems on unbounded domains , 1992 .

[25]  A. Ogata,et al.  Symmetric positive entire solutions of second-order quasilinear degenerate elliptic equations , 1994 .

[26]  Tomomitsu Teramoto.  On positive radial entire solutions of second-order quasilinear elliptic systems , 2003 .

[27]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[28]  R. S. Rodrigues.  On elliptic problems involving critical Hardy–Sobolev exponents and sign-changing function , 2010 .

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

[30]  Zoubin Ghahramani,et al.  Variational Methods , 2014, Computer Vision, A Reference Guide.

[31]  Caisheng Chen,et al.  Existence of multiple solutions for a singular quasilinear elliptic equation in RN , 2011, Comput. Math. Appl..