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Solutions and multiple solutions for p(x)-Laplacian equations with nonlinear boundary condition

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Abstract

The authors study the p(x)-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f 1(x, u), f 2(x, u) and h 1(x), h 2(x), such that the associated functional satisfies the “mountain pass lemma” and “fountain theorem” respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.

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Authors and Affiliations

  1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Zifei Shen & Chenyin Qian

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  1. Zifei Shen
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  2. Chenyin Qian
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Correspondence to Zifei Shen.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10771141) and the Zhejiang Provincial Natural Science Foundation of China (No. Y7080008).

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Shen, Z., Qian, C. Solutions and multiple solutions for p(x)-Laplacian equations with nonlinear boundary condition. Chin. Ann. Math. Ser. B 30, 397–412 (2009). https://doi.org/10.1007/s11401-008-0395-0

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  • DOI: https://doi.org/10.1007/s11401-008-0395-0

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