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- Title
EXISTENCE OF SOLUTIONS FOR P-KIRCHHOFF TYPE PROBLEMS WITH CRITICAL EXPONENT.
- Authors
HAMYDY, AHMED; MASSAR, MOHAMMED; TSOULI, NAJIB
- Abstract
We study the existence of solutions for the p-Kirchhoff type problem involving the critical Sobolev exponent, -[g(∫Ω|∇u|pdx)] Δpu = λf(x, u) + |u|p✭-2u in Ω, u = 0 on ∂Ω, where Ω is a bounded smooth domain of RN, 1 < p < N, p✭ = Np/(N - p) is the critical Sobolev exponent, λ is a positive parameter, f and g are continuous functions. The main results of this paper establish, via the variational method. The concentration-compactness principle allows to prove that the Palais-Smale condition is satisfied below a certain level.
- Subjects
SOBOLEV spaces; EXPONENTS; SMOOTHNESS of functions; BOUNDARY value problems; PARAMETER estimation
- Publication
Electronic Journal of Differential Equations, 2011, Vol 2011, p1
- ISSN
1550-6150
- Publication type
Article