국가지식-학술정보
DIRICHLET EIGENVALUE PROBLEMS UNDER MUSIELAK-ORLICZ GROWTH
- 대한수학회
- Journal of the Korean Mathematical Society
- Vol.59 No.6
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2022.011139 - 1151 (13 pages)
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DOI : 10.4134/JKMS.j210669
- 0
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This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem <TEX>$${-div;(frac{g(x,;{mid}{ abla}u{mid})}{{mid}{ abla}u{mid}}{ abla}u)={lambda};(frac{g(x,{mid}u{mid})}{{mid}u{mid}}u);in;{Omega}, \u;=;0;on;{partial}{Omega},$$</TEX> where Ω is a bounded domain in ℝ<sup>N</sup> 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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