Research article

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

  • 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

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  • 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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