| On Nonlocal Elliptic Systems of $p(x)$-Kirchhoff-Type under Neumann Boundary Condition |
| Received:February 08, 2012 Revised:September 04, 2012 |
| Key Words:
variational method elliptic systems nonlocal Neumann boundary.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11261052). |
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| Abstract: |
| This paper is concerned with the existence of solutions to a class of $p(x)$-Kirchhoff-type systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence of solutions for the problem. Since the Poincar\'{e}'s inequality does not hold in the space $W^{1,p(x)}(\Omega)$, we shall prove the Poincar\'{e}-Wirtinger's inequality in a subspace of $W^{1,p(x)}(\Omega)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.04.007 |
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