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Radially Symmetric Solutions of the p-Laplace Equation with Gradient Terms

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We consider the Dirichlet problem for the p-Laplace equation with nonlinear gradient terms. In particular, these gradient terms cannot satisfy the Bernstein—Nagumo conditions. We obtain some sufficient conditions that guarantee… Click to show full abstract

We consider the Dirichlet problem for the p-Laplace equation with nonlinear gradient terms. In particular, these gradient terms cannot satisfy the Bernstein—Nagumo conditions. We obtain some sufficient conditions that guarantee the existence of a global bounded radially symmetric solution without any restrictions on the growth of the gradient term. Also we present some conditions on the function simulating the mass forces, which allow us to obtain a bounded radially symmetric solution under presence of an arbitrary nonlinear source.

Keywords: laplace equation; radially symmetric; gradient terms; symmetric solutions

Journal Title: Journal of Applied and Industrial Mathematics
Year Published: 2018

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