Results 251 to 260 of about 92,595 (298)

On the Infinitely Many Solutions of a Semilinear Elliptic Equation

SIAM Journal on Mathematical Analysis, 1986
Die Autoren untersuchen sphärisch symmetrische Lösungen von \[ (*)\quad \Delta u+f(u)=0\quad im\quad {\mathbb{R}}^ n, \] wobei die Nichtlinearität f die folgenden Bedingungen erfüllt: (1) \(f\in C^ 1\); (2) \(f(u)=k(u)| u|^{\sigma}u+g(u)\) mit \(k(u)=k_+\), \(u\geq 0\); \(k(u)=k_-\), \(u0\), \(k_->0\) \(g(u)=O(| u|^{\gamma})\), \(g'(u)=O(| u|^{\gamma ...
Jones, C., Küpper, T.
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Singular Solutions for some Semilinear Elliptic Equations

Archive for Rational Mechanics and Analysis, 1987
This paper studies solutions \(u\in C\) \(2(B_ R\setminus 0)\) of the equation \(-\Delta u+u\) \(p=0\), \(u\geq 0\) on \(B_ R\setminus 0\), the dimension of the underlying space being N.
Brézis, Haïm, Oswald, Luc
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A class of semilinear elliptic equations on groups of polynomial growth

Journal of Differential Equations, 2023
B. Hua, Ruo Li, Lidan Wang
semanticscholar   +1 more source

Global Positive Solutions of Semilinear Elliptic Equations

Canadian Journal of Mathematics, 1983
The semilinear elliptic boundary value problem1.1will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where1.2Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded ...
Noussair, Ezzat S., Swanson, Charles A.
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Two sequences of solutions for the semilinear elliptic equations with logarithmic nonlinearities

Journal of Differential Equations, 2023
W. Shuai
semanticscholar   +1 more source

On the Existence of Positive Solutions of Semilinear Elliptic Equations

SIAM Review, 1982
In this paper we study the existence of positive solutions of semilinear elliptic equations. Various possible behaviors of nonlinearity are considered, and in each case nearly optimal multiplicity results are obtained. The results are also interpreted in terms of bifurcation diagrams.
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Nontrivial solutions of elliptic semilinear equations¶at resonance

manuscripta mathematica, 2000
The authors consider the following Dirichlet problem \(-\Delta u = \lambda_m +f(x,u)\) in a bounded domain \(\Omega\) with smooth boundary, where \(\lambda _m\) is an eigenvalue of the Laplacian operator in \(\Omega\) with Dirichlet boundary data. They treat the doubly resonant case, both at infinity and zero, \(\lim_{t\to 0}f(x,t)/t= \lim_{t\to \infty}
Perera, Kanishka, Schechter, Martin
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Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential

Israel Journal of Mathematics, 2016
We study a nonlinear equation in the half-space {x1 > 0} with a Hardy potential, specifically −Δu−μx12u+up=0inℝ+n,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
C. Bandle, M. Marcus, Vitaly Moroz
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On the iterative and minimizing sequences for semilinear elliptic equations (I)

Japan Journal of Industrial and Applied Mathematics, 1995
Les auteurs continuent leur précédente recherche [ibid. 12, No. 2, 309-326 (1995; Zbl 0842.35004)] sur la solution numérique de l'équation elliptique semilinéaire (1) \(-\Delta u= f(u)\) dans \(\Omega\), avec la condition (2) \(u=0\) sur \(\partial \Omega\), où \(\Omega\) est un domaine polygonal à deux dimension.
Mizutani, Akira, Suzuki, Takashi
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On Semilinear Elliptic Equations with Hardy-Leray Potentials

Tokyo Journal of Mathematics
Summary: This paper is concerned with a semilinear elliptic equation with the Hardy-Leray potential. We employ the method of moving planes to prove the radial symmetry of positive solutions. Based on this result, we obtain the Liouville theorem in subcritical case. In addition, we find special radial solutions in critical case. All the properties above
Li, Yayun, Lei, Yutian
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