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Vanational elliptic problems involving noncoercive functionals

Published online by Cambridge University Press:  14 November 2011

Miguel Ramos  and
Luis Sanchez
Miguel Ramos
Affiliation:
INIC/CMAF, Avenida Professor Gama Pinto, 2, 1699 Lisboa Codex, Portugal
Luis Sanchez
Affiliation:
INIC/CMAF, Avenida Professor Gama Pinto, 2, 1699 Lisboa Codex, Portugal
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Synopsis

We consider the nonlinear elliptic problem at resonance, Δu + λ1u + f(x, u) = h(x) in Ω, u = 0 on ∂Ω, where Ω is a bounded smooth domain in ℝN, λl is the first eigenvalue of –Δ in Ω and h(x) is orthogonal to the first eigenfunction. We give some conditions of solvability 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 112 , Issue 1-2 , 1989 , pp. 177 - 185
Copyright
Copyright © Royal Society of Edinburgh 1989

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