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	Certain classes of potentials for p-Laplacian to be non-degenerate
	Zhang, MR
	2010-05-06 ; 2010-05-06
关键词	p-Laplacian eigenvalue L-alpha norm boundary condition non-degeneracy stability DIFFERENTIAL-EQUATIONS EIGENVALUES NONRESONANCE Mathematics
中文摘要	Given a positive integer n and an exponent 1 <= alpha <= infinity. We will find explicitly the optimal bound r(n) such that if the L-alpha norm of a potential q(t) satisfies parallel to q parallel to(L alpha(I)) < r(n) then the n(th) Dirichlet eigenvalue of the one-dimensional p-Laplacian with the potential q(t): (vertical bar u'broken vertical bar(p-2)u')' + (gimel + q(t)) vertical bar u vertical bar(p-2)u = 0 (1 < p < infinity) will be positive. Using these bounds, we will construct, for the Dirichlet, the Neumann, the periodic or the antiperiodic boundary conditions, certain classes of potentials q(t) so that the p-Laplacian with the potential q(t) is non-degenerate, which means that the above equation with gimel = 0 has only the trivial solution verifying the corresponding boundary condition.
语种	英语 ; 英语
出版者	WILEY-V C H VERLAG GMBH ; WEINHEIM ; PO BOX 10 11 61, D-69451 WEINHEIM, GERMANY
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14185]
专题	清华大学
推荐引用方式 GB/T 7714	Zhang, MR. Certain classes of potentials for p-Laplacian to be non-degenerate[J],2010, 2010.
APA	Zhang, MR.(2010).Certain classes of potentials for p-Laplacian to be non-degenerate..
MLA	Zhang, MR."Certain classes of potentials for p-Laplacian to be non-degenerate".(2010).

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