Volume 27, Issue 3
Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain

Mohamed Amine Ben Boubaker

10.4208/jpde.v27.n3.2

J. Part. Diff. Eq., 27 (2014), pp. 200-216.

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  • Abstract

We find and prove 3G inequalities for the Laplacian Green function with the Dirichlet boundary condition, which are applied to show the existence of positive continuous solutions of the nonlinear equation Δu-Vu=g(⋅,u), where V and g are Borel measurable functions, required to satisfy suitable assumptions related to a new functional class J. Our approach uses the Schauder fixed point theorem.

  • History

Published online: 2014-09

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