Results 1 to 10 of about 75,181 (273)
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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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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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
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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 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
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Semilinear elliptic equations with critical nonlinearities [PDF]
Bulletin of the Australian Mathematical Society, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elliot Tonkes
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Isolated singularities of some semilinear elliptic equations
Journal of Differential Equations, 1985 The paper studies the existence and behavior of isolated singularities of solutions of the equation (1) \(-\Delta u(x)+g(u(x))=f(x)\) in a domain \(\Omega\subset R^ n\), \(n\geq 3\); g is a nondecreasing real function and \(f\in L^{\infty}(\Omega)\).
Juan Luís Vázquez +1 more
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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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Bubble towers for supercritical semilinear elliptic equations [PDF]
Journal of Functional Analysis, 2004 We construct positive solutions of the semilinear elliptic problem $ u+ u + u^p = 0$ with Dirichet boundary conditions, in a bounded smooth domain $ \subset \R^N$ $(N\geq 4)$, when the exponent $p$ is supercritical and close enough to $\frac{N+2}{N-2}$ and the parameter $ \in\R$ is small enough.
Yuxin Ge, Ruihua Jing, Frank Pacard
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Entire solutions of semilinear elliptic equations
Electronic Journal of Differential Equations, 2004 We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors.
Alexander Gladkov, Nickolai Slepchenkov
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