Results 11 to 20 of about 394,604 (313)
Regularity and Symmetry for Semilinear Elliptic Equations in Bounded Domains [PDF]
arXiv, 2021 In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are locally stable.
L. Dupaigne, A. Farina
arxiv +3 more sources
Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains [PDF]
Analysis & PDE 15 (2022) 551-566, 2019 We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
L. Dupaigne, A. Farina
arxiv +3 more sources
A remark on partial data inverse problems for semilinear elliptic equations [PDF]
arXiv, 2019 We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.
Katya Krupchyk, G. Uhlmann
arxiv +3 more sources
The Free Boundary of a Semilinear Elliptic Equation [PDF]
Transactions of the American Mathematical Society, 1984 The Dirichlet problem Δ u = λ f ( u ) \Delta u = \lambda \,f(u) in a domain Ω , u = 1 \Omega ,\,u = 1 on ∂ Ω \partial \Omega is considered with f ( t
Avner Friedman, Daniel Phillips
openaire +3 more sources
On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool.
Yang Zuodong
core +3 more sources
Uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities [PDF]
arXiv, 2008 We consider semilinear elliptic equations with double power nonlineaities. The condition to assure the existence of positive solutions is well-known. In the present paper, we remark that the additional condition to assure uniqueness proposed by Ouyang ...
Kawano, Shinji
core +5 more sources
Boundedness of stable solutions to semilinear elliptic equations: a survey [PDF]
, 2017 This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known $L^{\infty}$ estimates that hold for all nonlinearities.
Cabre, Xavier
core +9 more sources
On semilinear elliptic equations with diffuse measures [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2018 We consider semilinear equation of the form $-Lu=f(x,u)+ $, where $L$ is the operator corresponding to a transient symmetric regular Dirichlet form ${\mathcal E}$, $ $ is a diffuse measure with respect to the capacity associated with ${\mathcal E}$, and the lower-order perturbing term $f(x,u)$ satisfies the sign condition in $u$ and some weak ...
Andrzej Rozkosz, Tomasz Klimsiak
openaire +6 more sources
Semilinear elliptic equations and fixed points [PDF]
Proceedings of the American Mathematical Society, 2004 In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $ \subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.
Cleon S. Barroso
+6 more sources
On a Class of Semilinear Elliptic Equations in Rn
Journal of Differential Equations, 2002 AbstractWe establish that for n⩾3 and p>1, the elliptic equation Δu+K(x)up=0 in Rn possesses separated positive entire solutions of infinite multiplicity, provided that a locally Hölder continuous function K⩾0 in Rn\{0}, satisfies K(x)=O(∣x∣σ) at x=0 for some σ>−2, and K(x)=c∣x∣−2+O(∣x∣−n[log∣x∣]q) near ∞ for some constants c>0 and q>0.
Soohyun Bae, Tong Keun Chang
openaire +3 more sources