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AIMS Mathematics

2017, Volume 2, Issue 3: 400-421. doi: 10.3934/Math.2017.3.400
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Research article

The viscosity solutions of a nonlinear equation related to the p-Laplacian

  • School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. China
  • Received: 10 May 2017 Accepted: 25 May 2017 Published: 28 June 2017

  • The viscosity solutions of a nonlinear equation related to the p-Laplacian are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounded properties of the solutions and the Lp-norm for the gradients. By the compactness theorem, we prove the existence of the viscosity solution of the equation.

    Citation: Qitong Ou, Huashui Zhan. The viscosity solutions of a nonlinear equation related to the p-Laplacian[J]. AIMS Mathematics, 2017, 2(3): 400-421. doi: 10.3934/Math.2017.3.400

    Related Papers:

  • The viscosity solutions of a nonlinear equation related to the p-Laplacian are considered. Besides there is a damping term in the equation, a nonlocal function is added. By considering the regularized problem and using Moser iteration technique, we get the uniformly local bounded properties of the solutions and the Lp-norm for the gradients. By the compactness theorem, we prove the existence of the viscosity solution of the equation.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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