Results 1 to 10 of about 376,156 (276)
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
On Positive Solutions of Semilinear Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1987 This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem Δ u + f ( u ) = 0 , x ∈ Ω , u = 0 , x ∈ ∂ Ω \Delta u + f(u) = 0,x \in \Omega ,u = 0,x ...
E. N. Dancer, Klaus Schmitt
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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
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A dynamical approach to semilinear elliptic equations [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019 A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in \mathbb{R}^{n} is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for the PDE.
M. Beck +4 more
semanticscholar +5 more sources
On semilinear elliptic equations with diffuse measures [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2018 We consider semilinear equation of the form $$-Lu=f(x,u)+\mu $$-Lu=f(x,u)+μ, where L is the operator corresponding to a transient symmetric regular Dirichlet form $${\mathcal {E}}$$E, $$\mu $$μ is a diffuse measure with respect to the capacity associated
Tomasz Klimsiak, A. Rozkosz
semanticscholar +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
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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
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On the Cauchy problem for semilinear elliptic equations [PDF]
Journal of Inverse and Ill-posed Problems, 2016 We study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard.
N. Tuan +3 more
semanticscholar +3 more sources