Boundary singularities of semilinear elliptic equations with Leray-Hardy potential
نویسندگان
چکیده
We study existence and uniqueness of solutions ([Formula: see text]) [Formula: text] in text], on where is a bounded smooth domain such that constant, continuous nondecreasing function satisfying some integral growth condition two Radon measures, respectively, text]. show the situation differs considerably according measure concentrated at or not. When power we introduce capacity framework which provides necessary sufficient conditions for solvability problem text]).
منابع مشابه
Hardy-Sobolev Critical Elliptic Equations with Boundary Singularities
Unlike the non-singular case s = 0, or the case when 0 belongs to the interior of a domain Ω in IR(n ≥ 3), we show that the value and the attainability of the best Hardy-Sobolev constant on a smooth domain Ω, μs(Ω) := inf {
متن کامل”boundary Blowup” Type Sub-solutions to Semilinear Elliptic Equations with Hardy Potential
Semilinear elliptic equations which give rise to solutions blowing up at the boundary are perturbed by a Hardy potential μ/δ(x, ∂Ω). The size of this potential effects the existence of a certain type of solutions (large solutions): if μ is too small, then no large solution exists. The presence of the Hardy potential requires a new definition of large solutions, following the pattern of the asso...
متن کاملMeasure boundary value problems for semilinear elliptic equations with critical Hardy potentials
Article history: Received 16 October 2014 Accepted after revision 26 January 2015 Available online 26 February 2015 Presented by Haïm Brézis Let Ω ⊂ RN be a bounded C2 domain and Lκ = − − κ d2 where d = dist(., ∂Ω) and 0 < κ ≤ 4 . Let α± = 1 ± √ 1− 4κ , λκ the first eigenvalue of Lκ with corresponding positive eigenfunction φκ . If g is a continuous nondecreasing function satisfying ∫ ∞ 1 (g(s)...
متن کاملAsymptotic Behavior of Solutions to Semilinear Elliptic Equations with Hardy Potential
Let Ω be an open bounded domain in RN (N ≥ 3) with smooth boundary ∂Ω, 0 ∈ Ω. We are concerned with the asymptotic behavior of solutions for the elliptic problem: (∗) −∆u− μu |x|2 = f(x, u), u ∈ H 0 (Ω), where 0 ≤ μ < ( N−2 2 )2 and f(x, u) satisfies suitable growth conditions. By Moser iteration, we characterize the asymptotic behavior of nontrivial solutions for problem (∗). In particular, we...
متن کاملLarge Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity
On a bounded smooth domain Ω ⊂ R we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to ∂Ω. We derive global a priori bounds of the Keller–Osserman type. Using a Phragmen–Lindelöf alternative for generalized sub and super-harmonic functions we discuss existence, nonexistence and uniqueness of so-called large solut...
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: Communications in Contemporary Mathematics
سال: 2021
ISSN: ['0219-1997', '1793-6683']
DOI: https://doi.org/10.1142/s0219199721500516