Existence of renormalized solutions for nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces
Abstract
In this paper, we prove the existence of renormalized solutions for some class nonlinear elliptic problem of the type
−div a(x,u,∇u) + H(x,u,∇u) = µ − div φ(u),
in the Musielak-Orlicz-Sobolev spaces W10Lϕ(Ω). No ∆2−condition is assumed on the Musielak function. We assume that H(x,s,ξ) satisfies has a natural growth with respect to its third argument and satisfies the sign condition. The µ is assumed to belong to L1(Ω) + W−1Eψ(Ω) and φ(·) ∈ C0(IR,IRN) is a continuous function.Copyright © 2021 Mohammed Al-Hawmi, Mustafa Al-Hasisi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Al-Hawmi, M. Al-Hasisi, Existence of renormalized solutions for nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces, J. Math. Comput. Sci. 12 (2022), 23. https://doi.org/10.28919/jmcs/6590
BibTeX
@article{Al-Hawmi2022,
author = {Al-Hawmi, Mohammed and Al-Hasisi, Mustafa},
title = {Existence of renormalized solutions for nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {23},
doi = {10.28919/jmcs/6590}
}