AIMS Mathematics, 2017, 2(3): 400-421. doi: 10.3934/Math.2017.3.400.

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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

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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Keywords Nonlinear equation; p-Laplacian; moser iteration; viscosity solution

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

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