Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory | Zendy

Alves Claudianor O. | Zendy; Figueiredo Giovany M. | Zendy

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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.

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