TY - Type of reference
TI - [Forthcoming] Multiplicity of solutions for a nonhomogeneous problem involving a potential in Orlicz-Sobolev spaces
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 -
JF - Advances in Pure and Applied Mathematics
KW - Mountain pass Theorem, Ekeland’s variational principle, Orlicz-Sobolev space., Ekeland’s variational principle, Mountain pass Theorem, Orlicz-Sobolev space.,
L1 -
LA - en
PB - ISTE OpenScience
DA - 2020/09/14
SN - 1869-6090
TT - [Forthcoming] Multiplicité de solutions pour un problème non homogène impliquant un potentiel dans les espaces d’Orlicz-Sobolev
UR - https://www.openscience.fr/Multiplicity-of-solutions-for-a-nonhomogeneous-problem-involving-a-potential-in
IS -

Forthcoming papers
VL -
ER -