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Multi-bump nodal solutions for an indefinite non-homogeneous elliptic problem

Published online by Cambridge University Press:  08 July 2009

Pedro M. Girão
Affiliation:
Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal (pgirao@math.ist.utl.pt)
José Maria Gomes
Affiliation:
Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal (jgomes@math.ist.utl.pt)

Abstract

We construct multi-bump nodal solutions of the elliptic equation

in , when μ is large, under appropriate assumptions, for f superlinear and subcritical and such that the eigenvalues of the associated linearized operator on at zero, uu − λ(−Δ)−1(a+u), are positive. The solutions are of least energy in some Nehari-type set defined by imposing suitable conditions on orthogonal components of functions in .

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009

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