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Existence and Multiplicity of Solutions for p-Laplacian Neumann Problems

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Abstract

In this paper, existence theorems are proved for p-Laplacian Neumann problems under the Landesman–Lazer type condition. Our results are derived from a classical saddle point theorem and the least action principle respectively. Furthermore, multiplicity of solutions is established by applying a known multiple critical points result due to H. Brezis and L. Nirenberg. The above-mentioned conclusions are based on variational methods.

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Authors and Affiliations

  1. Department of Mathematics, Huanggang Normal University, Hubei, 438000, China

    Qin Jiang & Sheng Ma

  2. Department of Mathematics and Informatics, University of Oradea, University Street 1, 410087, Oradea, Romania

    Daniel Paşca

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  1. Qin Jiang
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  2. Sheng Ma
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  3. Daniel Paşca
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Correspondence to Daniel Paşca.

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Jiang, Q., Ma, S. & Paşca, D. Existence and Multiplicity of Solutions for p-Laplacian Neumann Problems. Results Math 74, 67 (2019). https://doi.org/10.1007/s00025-019-0995-x

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