Francisco Ortegón Gallego, Mohamed Rhoudaf, Hajar Talbi, On the existence of bilateral solutions to an anisotropic nonlinear coupled elliptic system

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DOI: 10.23952/jnva.9.2025.6.01

Volume 9, Issue 6, 1 December 2025, Pages 811-831

Abstract. The existence of a bilateral solution at a given height to the strongly nonlinear and degenerate problem $A(u)=\rho(u)|\nabla \varphi|^{2}$ , $\mathop{\rm div}(\rho(u) \nabla \varphi)=0$ in $\Omega$ , $u=0$ and $\varphi=\varphi_0$ on $\partial\Omega$ , where $A$ is a Leray-Lions operator, is proved in the framework of anisotropic Sobolev space. The bilateral solution is obtained through a double approximation process, with the first one being a penalization technique.

How to Cite this Article:
F.O. Gallego, M. Rhoudaf, H. Talbi, On the existence of bilateral solutions to an anisotropic nonlinear coupled elliptic system, J. Nonlinear Var. Anal. 9 (2025), 811-831.