Results 121 to 130 of about 92,595 (298)
On singular semilinear elliptic equations
, 1991 For the semilinear elliptic equation Δu + p(x)u⁻ʸ = 0, x ∈ Rⁿ, n ≥ 3, γ > 0, we show via the barrier method the existence of a positive entire solution behaving like |x|²⁻ⁿ near ∞.
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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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Inverse problems for fractional semilinear elliptic equations [PDF]
Nonlinear Analysis, 2020 Ru-Yu Lai, Yi-Hsuan Lin
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Solutions to nonlinear elliptic equations with a nonlocal boundary condition
Electronic Journal of Differential Equations, 2002 We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated.
Yuandi Wang
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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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Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations [PDF]
, 1997 Filippo Gazzola, Bernhard Ruf
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Separation Property of Solutions for a Semilinear Elliptic Equation
Journal of Differential Equations, 2000 The authors consider the problem of finding a positive solution \(u\) of the differential equation \(\Delta u + K(|x|)u^p = 0\) in \(\mathbb{R}^n\setminus \{0\}\). Here \(K\) is a given function which is Hölder continuous in \(\mathbb{R}^n\setminus \{0\}\). Many authors (often in collaboration with Li) have studied this problem under various hypotheses
Liu, Yi, Li, Yi, Deng, Yinbin
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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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The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation. [PDF]
J Geom Anal, 2023 Baumann P, Mazari-Fouquer I, Sturm K.
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On the positive, “radial” solutions of a semilinear elliptic equation in N$\mathbb {H}^N$ [PDF]
, 2012 Catherine Bandle, Yoshitsugu Kabeya
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