Existence of renormalized solutions for nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces

Mohammed Al-Hawmi, Mustafa Al-Hasisi

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.

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Published: 2021-11-30

How to Cite this Article:

Mohammed Al-Hawmi, Mustafa Al-Hasisi, Existence of renormalized solutions for nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces, J. Math. Comput. Sci., 12 (2022), Article ID 23

Copyright © 2022 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.

 

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