[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j210669

DIRICHLET EIGENVALUE PROBLEMS UNDER MUSIELAK-ORLICZ GROWTH

Benyaiche, Allami (Ibn Tofail University Department of Mathematics)
Khlifi, Ismail (Ibn Tofail University Department of Mathematics)

Publication Information

Journal of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1139-1151 More about this Journal

Abstract

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $\{-div\;$\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u$={\lambda}\;$\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u$\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

Keywords

Dirichlet eigenvalue problems; Lusternik-Schnirelmann principle; $G({\cdot})$ -Laplacian; Musielak-Orlicz growth; generalized $\Phi$ -function; generalized Orlicz-Sobolev space;

Citations & Related Records

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