DIRICHLET EIGENVALUE PROBLEMS UNDER MUSIELAK-ORLICZ GROWTH

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 ℝN...

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Veröffentlicht in:	Journal of the Korean Mathematical Society 2022, Vol.59 (6), p.1139-1151
Hauptverfasser:	Benyaiche, Allami, Khlifi, Ismail
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creator	Benyaiche, Allami Khlifi, Ismail
description	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 ℝN 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.
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title	DIRICHLET EIGENVALUE PROBLEMS UNDER MUSIELAK-ORLICZ GROWTH
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