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EXISTENCE AND BIFURCATION RESULTS FOR FOURTH-ORDER ELLIPTIC EQUATIONS INVOLVING TWO CRITICAL SOBOLEV EXPONENTS

Published online by Cambridge University Press:  01 January 2009

D. A. KANDILAKIS ,
M. MAGIROPOULOS  and
N. ZOGRAPHOPOULOS
D. A. KANDILAKIS
Affiliation:
Department of Sciences, Technical University of Crete, 73100 Chania, Greece e-mail: dimkand@gmail.com
M. MAGIROPOULOS
Affiliation:
Department of Sciences, Technological and Educational Institute of Crete, 71500 Heraklion, Greece e-mail: mageir@stef.teiher.gr
N. ZOGRAPHOPOULOS
Affiliation:
Department of Sciences, Technical University of Crete, 73100 Chania, Greece e-mail: nzogr@science.tuc.gr
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Abstract

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Let Ω be a smooth bounded domain in RN, with N ≥ 5. We provide existence and bifurcation results for the elliptic fourth-order equation Δ2u − Δpu = f(λ, x, u) in Ω, under the Dirichlet boundary conditions u = 0 and ∇u = 0. Here λ is a positive real number, 1 < p ≤ 2# and f(.,., u) has a subcritical or a critical growth s, 1 < s ≤ 2*, where and . Our approach is variational, and it is based on the mountain-pass theorem, the Ekeland variational principle and the concentration-compactness principle.

Keywords

35J3535B3335G2035B32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 127 - 141
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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