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A variational approach to multiplicity in elliptic problems near resonance*

Published online by Cambridge University Press:  14 November 2011

M. Ramos  and
L. Sanchez
M. Ramos
Affiliation:
CMAF, Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal
L. Sanchez
Affiliation:
CMAF, Faculdade de Ciências da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal
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Abstract

We consider the nonlinear elliptic problem ± (Δu + λu) + f(x, u) = h(x) in Ω, u = 0 on ∂Ω, where Ω is a bounded smooth domain in ℝN, λ is near the first eigenvalue and h(x) is orthogonal to the first eigenfunction. We give some conditions of existence of positive solutions and of multiple solutions in terms of the primitive of f with respect to u.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 385 - 394
Copyright
Copyright © Royal Society of Edinburgh 1997

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