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

Mohamed Amine Ben Boubaker

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

Published online: 2014-09

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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.

  • Keywords

Green function Schauder fixed point theorem superharmonic function

  • AMS Subject Headings

31A10 31A25 31A35 34B15 34B27 31C45 35J65

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COPYRIGHT: © Global Science Press

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@Article{JPDE-27-200, author = {}, title = {Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {3}, pages = {200--216}, 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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n3.2}, url = {http://global-sci.org/intro/article_detail/jpde/5137.html} }
TY - JOUR T1 - Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain JO - Journal of Partial Differential Equations VL - 3 SP - 200 EP - 216 PY - 2014 DA - 2014/09 SN - 27 DO - http://dor.org/10.4208/jpde.v27.n3.2 UR - https://global-sci.org/intro/jpde/5137.html KW - Green function KW - Schauder fixed point theorem KW - superharmonic function AB - 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.
Mohamed Amine Ben Boubaker . (2019). Positive Solutions of Nonlinear Elliptic Problem in a Non-Smooth Planar Domain. Journal of Partial Differential Equations. 27 (3). 200-216. doi:10.4208/jpde.v27.n3.2
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