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Infinitely many solutions for differential inclusion problems in \({\mathbb{R}^N}\) involving the \({p(x)}\)-Laplacian

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Abstract

In this paper we consider the differential inclusion problem in \({\mathbb{R}^N}\) involving the \({p(x)}\)-Laplacian of the type

$$-\triangle_{p(x)} u+V(x)|u|^{p(x)-2}u\in \partial F(x,u)\,\,\,{\rm {in}} \, \mathbb{R}^N.$$

Some new criteria to guarantee that the existence of infinitely many solutions for the considered problem is established by using the genus properties in nonsmooth critical point theory, which extend and complement previously known results in the literature.

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Authors and Affiliations

  1. Department of Applied Mathematics, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Bin Ge & Li-Li Liu

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  1. Bin Ge
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  2. Li-Li Liu
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Correspondence to Bin Ge.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11201095), the Youth Scholar Backbone Supporting Plan Project of Harbin Engineering University (No. 307201411008), the Fundamental Research Funds for the Central Universities (No. 2016), the Postdoctoral Research Startup Foundation of Heilongjiang (No. LBH-Q14044), the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province (No. LC201502).

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Ge, B., Liu, LL. Infinitely many solutions for differential inclusion problems in \({\mathbb{R}^N}\) involving the \({p(x)}\)-Laplacian. Z. Angew. Math. Phys. 67, 8 (2016). https://doi.org/10.1007/s00033-015-0612-0

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  • DOI: https://doi.org/10.1007/s00033-015-0612-0

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