Results 21 to 30 of about 92,595 (298)
AIMS Mathematics, 2022 This paper aims to construct a two-grid mixed finite element scheme for distributed optimal control governed by semilinear elliptic equations. The state and co-state are approximated by the $ P_0^2 $-$ P_1 $ pair and the control variable is approximated ...
Changling Xu, Hongbo Chen
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On Positive Solutions of Semilinear Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1987 This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem Δ u + f ( u ) = 0 , x ∈ Ω , u = 0 , x ∈ ∂ Ω \Delta u + f(u) = 0,x \in \Omega ,u = 0,x ...
Dancer, E. N., Schmitt, Klaus
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A Concentration Phenomenon for Semilinear Elliptic Equations [PDF]
Archive for Rational Mechanics and Analysis, 2012 For a domain $ \subset\dR^N$ we consider the equation $ - u + 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 $ $ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in $ as $n\to\infty ...
Ackermann, Nils, Szulkin, Andrzej
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Solutions of Semilinear Elliptic Equations in Tubes [PDF]
Journal of Geometric Analysis, 2012 Given a smooth compact k-dimensional manifold embedded in $\mathbb {R}^m$, with m\geq 2 and 1\leq k\leq m-1, and given >0, we define B_ ( ) to be the geodesic tubular neighborhood of radius about . In this paper, we construct positive solutions of the semilinear elliptic equation u + u^p = 0 in B_ ( ) with u = 0 on \partial B_ ...
Frank Pacard +2 more
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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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Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ [PDF]
Acta Mathematica, 2019 In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension $n \leq 9$. This result, that was only known to be true for $n\leq4$, is optimal: $\log(1/|x|^2)$
X. Cabré +3 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 domain in R N {\mathbb {R}^N} , N ⩾ 1 N \geqslant 1 . We consider the problem of finding nontrivial solutions to the elliptic boundary value problem \[
del Pino, Manuel A., Felmer, Patricio L.
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A remark on partial data inverse problems for semilinear elliptic equations [PDF]
Proceedings of the American Mathematical Society, 2019 We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.
Katya Krupchyk, G. Uhlmann
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Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations [PDF]
Revista matemática iberoamericana, 2019 We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique introduced in [LLS 19, FO19].
M. Lassas +3 more
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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.
Iguernane, Mohamed +4 more
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