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Increase of power leads to a bilateral solution to a strongly nonlinear elliptic coupled system
- Source :
- Advanced Nonlinear Studies, Vol 24, Iss 3, Pp 637-656 (2024)
- Publication Year :
- 2024
- Publisher :
- De Gruyter, 2024.
-
Abstract
- In this paper, we analyze the following nonlinear elliptic problem A(u)=ρ(u)|∇φ|2 in Ω,div(ρ(u)∇φ)=0 in Ω,u=0 on ∂Ω,φ=φ0 on ∂Ω. $\begin{cases}A\left(u\right)=\rho \left(u\right)\vert \nabla \varphi {\vert }^{2}\,\text{in}\,{\Omega},\quad \hfill \\ \text{div}\left(\rho \left(u\right)\nabla \varphi \right)=0\,\text{in}\,{\Omega},\quad \hfill \\ u=0\,\text{on}\,\partial {\Omega},\quad \hfill \\ \varphi ={\varphi }_{0}\,\text{on}\,\partial {\Omega}.\quad \hfill \end{cases}$ where A(u) = −div a(x, u, ∇u) is a Leray-Lions operator of order p. The second member of the first equation is only in L 1(Ω). We prove the existence of a bilateral solution by an approximation procedure, the keypoint being a penalization technique.
Details
- Language :
- English
- ISSN :
- 21690375 and 20230133
- Volume :
- 24
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Advanced Nonlinear Studies
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.0c1254398b2043b1aeea3d8afbf7e7e4
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/ans-2023-0133