Electron. J. Diff. Equ., Vol. 2011 (2011), No. 137, pp. 1-13.

Existence of solutions for nonlocal elliptic systems with nonstandard growth conditions

Guowei Dai

This article concerns the existence and multiplicity of solutions for a p(x)-Kirchhoff-type systems with Dirichlet boundary condition. By a direct variational approach and the theory of the variable exponent Sobolev spaces, under growth conditions on the reaction terms, we establish the existence and multiplicity of solutions.

Submitted July 9, 2011. Published October 19, 2011.
Math Subject Classifications: 35D05, 35J60, 35J70.
Key Words: Variational method; nonlinear elliptic systems; nonlocal condition.

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Guowei Dai
Department of Mathematics
Northwest Normal University
Lanzhou, 730070, China
email: daiguowei@nwnu.edu.cn

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