Concentration for an elliptic equation with singular nonlinearity
نویسندگان
چکیده
منابع مشابه
Rupture Solutions of an Elliptic Equation with a Singular Nonlinearity
We construct infinitely many non-radial rupture solutions of the equation ∆u = 1 up in RN\{0}, u(0) = 0, N ≥ 3 with p > pc(N − 1) := N − 1− 2 √ N − 2 2 √ N − 2− (N − 5) .
متن کاملHausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity
We consider the following semilinear elliptic equation with singular nonlinearity: u ? 1 u + h(x) = 0 in where > 1; h(x) 2 C 1 (() and is an open subset in R n ; n 2. Let u 2 C 0 (() be a nonnegative nite energy stationary solution and = fx 2 ju(x) = 0g be the rupture set of u. We show that the Hausdorr dimension of is less than or equal to (n?2)+(n+2) +1 .
متن کاملBifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurca...
متن کاملAn Elliptic Equation with No Monotonicity Condition on the Nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was o...
متن کاملPositive Solutions for Elliptic Equations with Singular Nonlinearity
We study an elliptic boundary-value problem with singular nonlinearity via the method of monotone iteration scheme: −∆u(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, where ∆ is the Laplacian operator, Ω is a bounded domain in RN , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. We prove the existence and the uniqueness of positive solutions under a set of hy...
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 de Mathématiques Pures et Appliquées
سال: 2012
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2011.02.001