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Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

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Abstract

We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.

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Acknowledgements

This work was supported by the National Research Foundation of Korea Grant Funded by the Korea Government (Grant No. NRF-2015R1D1A3A01019789).

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Authors and Affiliations

  1. Department of Mathematics, University of Ulsan, Ulsan, 680-749, South Korea

    Ky Ho & Inbo Sim

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  1. Ky Ho
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  2. Inbo Sim
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Correspondence to Inbo Sim.

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Ho, K., Sim, I. Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators. Sci. China Math. 60, 133–146 (2017). https://doi.org/10.1007/s11425-015-0385-0

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