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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