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 -