Results 41 to 50 of about 75,181 (273)
On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 Assume that Ω is a regular domain in the complex plane ℂ, and A(z) is a symmetric 2×2 matrix with measurable entries, det A = 1, and such that 1/K|ξ|2 ≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|2, ξ ∈ ℝ2, 1 ≤ K < ∞. We study the blow-up problem for a model semilinear equation div (A(z)∇u) = eu in Ω and show that the well-known Liouville–Bieberbach function solves the problem ...
Gutlyanskii, V.Y. +2 more
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Weak solutions of semilinear elliptic equations with Leray-Hardy potentials and measure data [PDF]
Mathematics in Engineering, 2019 We study existence and stability of solutions of (E 1) −∆u + µ |x| 2 u + g(u) = ν in Ω, u = 0 on ∂Ω, where Ω is a bounded, smooth domain of R N , N ≥ 2, containing the origin, µ ≥ − (N −2) 2 4 is a constant, g is a nondecreasing function satisfying some ...
L. Véron, Huyuan Chen
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Semilinear elliptic equations with Hardy potential and gradient nonlinearity [PDF]
Revista matemática iberoamericana, 2019 Let $\Omega \subset {\mathbb R}^N$ ($N \geq 3$) be a $C^2$ bounded domain and $\delta$ be the distance to $\partial \Omega$. We study positive solutions of equation (E) $-L_\mu u+ g(|\nabla u|) = 0$ in $\Omega$ where $L_\mu=\Delta + \frac{\mu}{\delta^2} $
K. Gkikas, P. Nguyen
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On singular solutions for a semilinear elliptic equation [PDF]
Kodai Mathematical Journal, 1995 Let \(\Omega\) be a bounded open set in \(\mathbb{R}^n\) with a smooth boundary \(\Gamma\), \(\Sigma\) be a smooth compact \(m\)-dimensional manifold in \(\Omega\) and \(\alpha(x)> 0\) be in \(C^\infty(\Omega)\). The author considers the problem \[ - \Delta u= u^p+ \delta_\Sigma,\quad 0< u\in C^2(\Omega- \Sigma).
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Risks, 2020 In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures. An example of such a risk measure is the expected discounted future dividend payments.
Stefan Kremsner +2 more
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Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions [PDF]
Set-Valued and Variational Analysis, 2017 Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence ’simple’ controls, with few jumps. Existence of optimal controls,
E. Casas, K. Kunisch
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Note on singular semilinear elliptic equations [PDF]
Hiroshima Mathematical Journal, 1992 This note deals with the existence of positive entire solution of the following singular semilinear elliptic equation \[ -\Delta u+c(x)u= p(x)u^{-\gamma}, \quad \text{in } \mathbb{R}^ n, \quad n\geq 3,\quad \gamma>0,\tag{1} \] where \(c\), \(p\) are locally Hölder continuous in \(\mathbb{R}^ n\) with exponent ...
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Semilinear elliptic equations on rough domains
Journal of Differential Equations, 2023 39 ...
Wolfgang Arendt, Daniel Daners
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On a class of semilinear elliptic problems near critical growth
International Journal of Mathematics and Mathematical Sciences, 1998 We use Minimax Methods and explore compact embedddings in the context of Orlicz and Orlicz-Sobolev spaces to get existence of weak solutions on a class of semilinear elliptic equations with nonlinearities near critical growth. We consider both biharmonic
J. V. Goncalves, S. Meira
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Symmetry breaking and semilinear elliptic equations
Journal of Computational and Applied Mathematics, 1989 Symmetry breaking bifurcations (SBB's) are studied which occur on the radially symmetric solution branches of the semilinear elliptic equation \(\Delta u+\lambda f(u)=0\) on the unit ball in the space \(R^ 3\). A general theory is developed which permits a straightforward calculation of the SBB's.
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