Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in RN

Abstract In this paper we study the elliptic system of gradient type with nonstandard growth conditions in R N . Existence and multiplicity results, under two growth conditions on the reaction terms, are established.

[1]  Xianling Fan,et al.  Sobolev Embedding Theorems for Spaces Wk, p(x)(Ω) , 2001 .

[2]  Giuseppe Mingione,et al.  Regularity Results for a Class of Functionals with Non-Standard Growth , 2001 .

[3]  J. Serrin,et al.  Existence and Uniqueness of Nonnegative Solutions of Quasilinear Equations inRn , 1996 .

[4]  Xianling Fan,et al.  On the Spaces Lp(x)(Ω) and Wm, p(x)(Ω) , 2001 .

[5]  M. Růžička.  Flow of shear dependent electrorheological fluids , 1999 .

[6]  Qihu Zhang,et al.  Existence of solutions for p(x) -Laplacian dirichlet problem , 2003 .

[7]  K Fan,et al.  Minimax Theorems. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[8]  V. Zhikov,et al.  AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY , 1987 .

[9]  Jiří Rákosník,et al.  Sobolev embeddings with variable exponent , 2000 .

[10]  D. Edmunds,et al.  Sobolev Embeddings with Variable Exponent, II , 2002 .

[11]  Xianling Fan,et al.  Existence and multiplicity of solutions for p(x)-Laplacian equations in RN , 2004 .

[12]  Jiří Rákosník,et al.  On spaces $L^{p(x)}$ and $W^{k, p(x)}$ , 1991 .

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

[14]  Xianling Fan,et al.  Existence and multiplicity of solutions for p(x)p(x)-Laplacian equations in RNRN☆ , 2004 .

[15]  Xianling Fan,et al.  Compact Imbedding Theorems with Symmetry of Strauss–Lions Type for the Space W1, p(x)(Ω) , 2001 .

[16]  A. El Hamidi,et al.  Existence results to elliptic systems with nonstandard growth conditions , 2004 .

[17]  Paolo Marcellini.  Regularity and existence of solutions of elliptic equations with p,q-growth conditions , 1991 .