Ouidad Azraibi, Said Ait Dada Alla, Badr El Haji, On some Nonlinear elliptic problems with boundary conditions in generalized Sobolev spaces, Vol. 2024 (2024), Article ID 19, pp. 1-8

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DOI: 10.23952/jnfa.2024.19

Received March 13, 2024; Accepted September 7, 2024; Published October 1, 2024

Abstract. The aim of this paper is to establish existence results for the following anisotropic elliptic equation $-div B(x, \vartheta, \nabla \vartheta)=f- div F$ , where the datum $f \in L^1(\Omega)$ and $F \in \prod_{i=1}^N L^{p_i^{\prime}}\left(\Omega, w_i^*\right)$ . Furthermore, only the large monotonicity conditions are assumed on $B(x, s, \xi)$ . To overcome this difficulty, we use the approach of Minty’s lemma in the anisotropic weighted Sobolev spaces.

How to Cite this Article:
O. Azraibi, S. Ait Dada Alla, B. El Haji, On some Nonlinear elliptic problems with boundary conditions in generalized Sobolev spaces, J. Nonlinear Funct. Anal. 2024 (2024) 19.