TY  - Type of reference 
TI  - Multiplicité de solutions pour un problème non homogène impliquant un potentiel dans les espaces d’Orlicz-Sobolev 
AU  - NAWAL IRZI 
AB  - This paper is devoted to the study of the nonhomogeneous problem
$$$
-div (a(|\nabla u|)\nabla u)+a(| u|)u=\lambda V(x)|u|^{m(x)-2}u-\mu g(x,u) \mbox{ in} \  \Omega,  \   u=0  \mbox{ on} \  \partial\Omega ,$$$ where $$$\Omega$$$ is a bounded smooth domain in $$$\mathbb{R}^N,\lambda, \mu$$$ are positive real numbers, $$$V(x)$$$ is a potential, $$$  m: \overline{ \Omega} \to (1, \infty)$$$ is a continuous function, $$$a$$$ is  mapping such that $$$ \varphi(|t|)t$$$  is increasing homeomorphism from ℝ to ℝ and $$$g: \overline{\Omega}\times ℝ \to ℝ$$$ is a continuous function. We establish there main results with various assumptions, the first one asserts that any $$$\lambda$$$0> is an eigenvalue of our problem. The second Theorem states the existence of a constant $$$\lambda^{*}$$$  such that every $$$\lambda \in (0,\lambda^{*})$$$ is an eigenvalue of the problem. While the third Theorem claims the existence of a constant $$$\lambda^{**}$$$ such that every $$$\lambda \in [\lambda^{**},\infty)$$$ is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces. 
DO  - 10.21494/ISTE.OP.2021.0722 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  -  Ekeland’s variational principle, Mountain pass Theorem,  Orlicz-Sobolev space., Mountain pass Theorem,  Ekeland’s variational principle,  Orlicz-Sobolev space.,  
L1  - http://www.openscience.fr/IMG/pdf/iste_apam21v12n3_1.pdf 
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2021/09/6 
SN  - 1869-6090 
TT  - Multiplicity of solutions for a  nonhomogeneous  problem involving a potential  in Orlicz-Sobolev spaces 
UR  - http://www.openscience.fr/Multiplicite-de-solutions-pour-un-probleme-non-homogene-impliquant-un-potentiel 
IS  - Numéro 3 (Septembre 2021) 
VL  - 12 
ER  -