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Sign changing solutions for elliptic equations with critical growth in cylinder typedomains

Published online by Cambridge University Press:  15 September 2002

Pedro Girão  and
Miguel Ramos
Pedro Girão
Affiliation:
Mathematics Department, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal; girao@math.ist.utl.pt.
Miguel Ramos
Affiliation:
CMAF and Faculty of Sciences, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal; mramos@lmc.fc.ul.pt.
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Abstract

We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, $u\in {\rm H_0^1}(\Omega)$, where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of $\mathbb{R}^N$ lying between two infinite cylinders.

Keywords

Nodal solutionscylindrical domainssemilinear elliptic equationcritical Sobolev exponentcon cen tra tion-compactness.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 407 - 419
Copyright
© EDP Sciences, SMAI, 2002

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References

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