Existence of renormalized solutions for some quasilinear elliptic Neumann problems
| Autor: | Idrissa Ibrango, Stanislas Ouaro, Mohamed Badr Benboubker, Hassane Hjiaj |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Numerical Analysis Applied Mathematics neumann problem Mathematics::Analysis of PDEs 35d05 35j60 renormalized solution QA1-939 Neumann boundary condition anisotropic variable exponent sobolev spaces strongly nonlinear elliptic equations Mathematics Analysis Mathematical physics |
| Zdroj: | Nonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 180-206 (2021) |
| ISSN: | 2353-0626 |
| DOI: | 10.1515/msds-2020-0133 |
| Popis: | This paper is devoted to study some nonlinear elliptic Neumann equations of the type{Au+g(x,u,∇u)+|u|q(⋅)-2u=f(x,u,∇u)inΩ,∑i=1Nai(x,u,∇u)⋅ni=0on∂Ω,\left\{ {\matrix{ {Au + g(x,u,\nabla u) + |u{|^{q( \cdot ) - 2}}u = f(x,u,\nabla u)} \hfill & {{\rm{in}}} \hfill & {\Omega ,} \hfill \cr {\sum\limits_{i = 1}^N {{a_i}(x,u,\nabla u) \cdot {n_i} = 0} } \hfill & {{\rm{on}}} \hfill & {\partial \Omega ,} \hfill \cr } } \right.in the anisotropic variable exponent Sobolev spaces, whereAis a Leray-Lions operator andg(x,u, ∇u),f(x,u, ∇u) are two Carathéodory functions that verify some growth conditions. We prove the existence of renormalized solutions for our strongly nonlinear elliptic Neumann problem. |
| Databáze: | OpenAIRE |
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