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Certain classes of potentials for p -Laplacian to be non-degenerate by Meirong Zhang is a Mathematics article available to read on EtoBox.
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## Abstract Given a positive integer __n__ and an exponent 1 ≤ __α__ ≤ ∞. We will find explicitly the optimal bound __r~n~__ such that if the __L^α^__ norm of a potential __q__ (__t__ ) satisfies ‖__q__ ‖ < __r~n~__ then the __n__ ^th^ Dirichlet eigenvalue of the onedimensional __p__ ‐Laplacian with the potential __q__ (__t__ ): (|__u__ ′|^__p__ –2^ __u__ ′)′ + (__λ__ + __q__ (__t__ )) |__u__ |^__p__ –2^__u__ = 0 (1 < __p__ < ∞) 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 __λ__ = 0 has only the trivial solution verifying the corresponding boundary condition. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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- Author
- Meirong Zhang
- Publisher
- John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)
- Published
- 2005
- Language
- EN
- Field
- Mathematics (Physical Sciences)