On the critical dimension of a fourth order elliptic problem with negative exponent
نویسندگان
چکیده
منابع مشابه
On the critical dimension of a fourth order elliptic problem with negative exponent
We study the regularity of the extremal solution of the semilinear biharmonic equation β∆u−τ∆u = λ (1−u)2 on a ball B ⊂ R , under Navier boundary conditions u = ∆u = 0 on ∂B, where λ > 0 is a parameter, while τ > 0, β > 0 are fixed constants. It is known that there exists a λ∗ such that for λ > λ∗ there is no solution while for λ < λ∗ there is a branch of minimal solutions. Our main result asse...
متن کاملConcentration Phenomena for Fourth-order Elliptic Equations with Critical Exponent
We consider the nonlinear equation ∆u = u n+4 n−4 − εu with u > 0 in Ω and u = ∆u = 0 on ∂Ω. Where Ω is a smooth bounded domain in Rn, n ≥ 9, and ε is a small positive parameter. We study the existence of solutions which concentrate around one or two points of Ω. We show that this problem has no solutions that concentrate around a point of Ω as ε approaches 0. In contrast to this, we construct ...
متن کاملMultiplicity of solutions for a fourth order elliptic equation with critical exponent on compact manifolds
This work deals with a perturbation of the so called prescribed scalar Q-curvature type equations on compact Riemannian manifolds; these equations are fourth order elliptic and of critical Sobolev growth. Sufficient conditions are given for having at least two distinct solutions. c © 2006 Elsevier Ltd. All rights reserved.
متن کاملElliptic Equations with Critical Exponent
where As3 is the Laplace-Beltrami operator on B' . Let 0* C (0, 7r) be the radius o r B ' , i.e., the geodesic distance of the North pole to OBq The values 0 < 0* < 7r/2 correspond to a spherical cap contained in the Northern hemisphere, 0* -7r/2 corresponds to B ~ being the Northern hemisphere and the values rr/2 < 0* < ~c correspond to a spherical cap which covers the Northern hemisphere. Fin...
متن کاملOn the spectrum of a fourth order nonlinear eigenvalue problem with variable exponent and indefinite potential
The present paper deals with the spectrum of a fourth order nonlinear eigenvalue problem involving variable exponent conditions and a sign-changing potential. The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that every λ ∈ [λ1,+∞) is an eigenvalue, while λ ∈ (−∞, λ0) cannot be an eigenvalue of the above problem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2010
ISSN: 0022-0396
DOI: 10.1016/j.jde.2009.09.011