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Existence of Solutions for Asymptotically ‘Linear’ p ‐Laplacian Equations
Author(s) -
Liu Shibo,
Li Shujie
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002546
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematics subject classification , limit (mathematics) , laplace operator , morse theory , morse code , p laplacian , pure mathematics , mathematical analysis , boundary value problem , physics , quantum mechanics , electrical engineering , engineering
Under very general conditions, a proof is given, via Morse theory, of the existence of solutions for asymptotically ‘linear’ p ‐Laplacian equations, where the asymptotic limit may be greater than the second eigenvalue. The existence of nonzero solutions is also considered. 2000 Mathematics Subject Classification 35J65, 58E05.