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Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory
Author(s) -
Alves Claudianor O.,
Figueiredo Giovany M.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2618
Subject(s) - biharmonic equation , mathematics , multiplicity (mathematics) , bounded function , class (philosophy) , pure mathematics , mathematical analysis , topology (electrical circuits) , boundary value problem , combinatorics , computer science , artificial intelligence
In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of biharmonic problemΔ 2 u = μ | u | q − 2 u + | u |2 蜧 蜧 − 2 u in Ω ,u = ∂u ∂η = 0 on∂Ω , where Ω ⊂ R Nis a bounded domain with smooth boundary. Using the Lusternik–Schnirelman theory, we relate the number of solutions with the topology of Ω. Copyright © 2012 John Wiley & Sons, Ltd.