Existence of a weak bounded solution for nonlinear degenerate elliptic equations in Musielak-Orlicz spaces

• Published in: Moroccan journal of pure and applied analysis Vol. 6; no. 1; pp. 16 - 33
• Main Authors: Bourahma, M., Bennouna, J., El Moumni, M.
• Format: Journal Article
• Language: English
• Published: Sciendo 01-06-2020
• Subjects: Bounded solutions; Elliptic equations; estimates; l∞ -estimates; Musielak-Orlicz-Sobolev spaces; Primary; 35J70, 35J87; Secondary; 46E30
• ISSN: 2351-8227; 2351-8227
• DOI: 10.2478/mjpaa-2020-0002

In this paper, we show the existence of solutions for the nonlinear elliptic equations of the form
where
and
: ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term
belongs to
(Ω) or to
(Ω), with
for some
> 0 and
is a Musielak function satisfying the Δ
-condition.