Results 1 to 10 of about 2,254 (236)
Topological Derivatives for Semilinear Elliptic Equations [PDF]
International Journal of Applied Mathematics and Computer Science, 2009 Topological Derivatives for Semilinear Elliptic EquationsThe form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in theL∞norm are obtained.
Mohamed Iguernane +4 more
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Nondegeneracy of the bubble solutions for critical equations involving the polyharmonic operator
Boundary Value Problems, 2023 We reprove a result by Bartsch, Weth, and Willem (Calc. Var. Partial Differ. Equ. 18(3):253–268, 2003) concerning the nondegeneracy of bubble solutions for a critical semilinear elliptic equation involving the polyharmonic operator.
Dandan Yang +3 more
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On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 This paper deals with the blow-up problem for a model semilinear equation of the type \[ \text{div}(A(z)\nabla u)= e^u \] in a simply connected domain \(\Omega\subset \mathbb{C}^1\). \(A(z)\) is a \(2\times 2\) symmetric uniformly elliptic matrix with measurable entries and \(\text{det\,}A=1\).
Gutlyanskii, V.Y. +2 more
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Solutions of Semilinear Elliptic Equations in Tubes [PDF]
Journal of Geometric Analysis, 2012 Given a smooth compact k-dimensional manifold Λembedded in $\mathbb {R}^m$, with m\geq 2 and 1\leq k\leq m-1, and given ε>0, we define B_ε(Λ) to be the geodesic tubular neighborhood of radius εabout Λ. In this paper, we construct positive solutions of the semilinear elliptic equation Δu + u^p = 0 in B_ε(Λ) with u = 0 on \partial B_ε(Λ), when the ...
Frank Pacard +2 more
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Multiple solutions for a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1995 Let Ω \Omega be a bounded, smooth ...
del Pino, Manuel A., Felmer, Patricio L.
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Semilinear problems with bounded nonlinear term
Boundary Value Problems, 2005 We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term.
Martin Schechter
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A Concentration Phenomenon for Semilinear Elliptic Equations [PDF]
Archive for Rational Mechanics and Analysis, 2012 For a domain $Ω\subset\dR^N$ we consider the equation $ -Δu + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $Ω$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\inΩ$ as $n\to\infty$.
Ackermann, Nils, Szulkin, Andrzej
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The structure of solutions of a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1992 We give a complete classification of solutions of the elliptic equation Δ u
Cheng, Kuo-Shung, Lin, Tai-Chia
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 The basic boundary value problems for semilinear equations of elliptic type with a spectral parameter and discontinuous nonlinearity are considered in a bounded domain with a sufficiently smooth boundary.
Dmitrij К Potapov
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On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations
International Journal of Mathematics and Mathematical Sciences, 2006 Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool.
Yang Zuodong
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