Geodesic
EXISTENCE AND BIFURCATION RESULTS FOR FOURTH-ORDER ELLIPTIC EQUATIONS INVOLVING TWO CRITICAL SOBOLEV EXPONENTS
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 127-141

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DOI

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.
DOI : 10.1017/S0017089508004588
Mots-clés : 35J35, 35B33, 35G20, 35B32 
KANDILAKIS, D. A.; MAGIROPOULOS, M.; ZOGRAPHOPOULOS, N. EXISTENCE AND BIFURCATION RESULTS FOR FOURTH-ORDER ELLIPTIC EQUATIONS INVOLVING TWO CRITICAL SOBOLEV EXPONENTS. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 127-141. doi: 10.1017/S0017089508004588
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     author = {KANDILAKIS, D. A. and MAGIROPOULOS, M. and ZOGRAPHOPOULOS, N.},
     title = {EXISTENCE {AND} {BIFURCATION} {RESULTS} {FOR} {FOURTH-ORDER} {ELLIPTIC} {EQUATIONS} {INVOLVING} {TWO} {CRITICAL} {SOBOLEV} {EXPONENTS}},
     journal = {Glasgow mathematical journal},
     pages = {127--141},
     year = {2009},
     volume = {51},
     number = {1},
     doi = {10.1017/S0017089508004588},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004588/}
}
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