Results 101 to 110 of about 1,398 (233)
On the Gierer-Meinhardt System with Saturation
, 2004 We consider the following shadow Gierer-Meinhardt system with saturation: \left\{\begin{array}{l} A_t=\epsilon^2 \Delta A -A + \frac{A^2}{ \xi (1+k A^2)} \ \ \mbox{in} \ \Omega \times (0, \infty),\\ \tau \xi_t= -\xi +\frac{1}{|\Omega|} \int_\Om A^2 ...
Winter, M, Wei, J
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Classification of positive solutions of semilinear elliptic equations
Comptes Rendus. Mathématique, 2003 We give a classification of all solutions of a general semilinear PDE in the positive quadrant of ℝ 2 .
Busca, J, Efendiev, M, Zelik, S
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Concentration and dynamic system of solutions for semilinear elliptic equations
Electronic Journal of Differential Equations, 2003 In this article, we use the concentration of solutions of the semilinear elliptic equations in axially symmetric bounded domains to prove that the equation has three positive solutions. One solution is y-symmetric and the other are non-axially symmetric.
Tsung-fang Wu
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An inverse boundary-value problem for semilinear elliptic equations
Electronic Journal of Differential Equations, 2010 We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded ...
Ziqi Sun
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Abstract and Applied Analysis, 2011 Existence and multiplicity of positive solutions for the following semilinear elliptic equation: −Δ𝑢+𝑢=𝑎(𝑥)|𝑢|𝑝−2𝑢+𝜆𝑏(𝑥)|𝑢|𝑞−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), are established, where 𝜆>0 ...
Tsing-San Hsu
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Karpatsʹkì Matematičnì Publìkacìï, 2018 A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary value problem the transition to an ...
M.V. Sidorov
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Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
Journal of Mathematical Analysis and Applications, 2000 It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser.
Liu, Shui-Qiang +2 more
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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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New multiple positive solutions for elliptic equations with singularity and critical growth
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation $ -\Delta u=\frac{\lambda}{u^\gamma}+u^{2^*-1},~x\in\Omega,~u=0, x\in\partial\Omega$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$
Hongmin Suo, Chunyu Lei, Jia-Feng Liao
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Nonexistence results for solutions of semilinear elliptic equations
Duke Mathematical Journal, 1994 Consider the semilinear elliptic equation (1) \(\Delta u= f(| x|)u+ g(x) u^ q\), \(x\in \mathbb{R}_ 0^ N\) for \(N\geq 3\), \(q>1\), where \(\mathbb{R}_ 0^ N= \mathbb{R}^ N\setminus \{0\}\), \(f\in L^ 1_{\text{loc}} (\mathbb{R}_ 0^ +)\), \(g\in L^ \infty_{\text{loc}} (\mathbb{R}_ 0^ N)\), \(g\geq 0\). The main theorems are sufficient conditions on \(f\)
BENGURIA, RD, LORCA, S, YARUR, CS
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