Results 21 to 30 of about 93,033 (295)
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities [PDF]
Mathematical Research Letters, 2019 We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\Omega)$.
Katya Krupchyk, G. Uhlmann
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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 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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Local minimizers in spaces of symmetric functions and applications [PDF]
, 2014 We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$.
Dos Santos +3 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 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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Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains [PDF]
Analysis & PDE, 2019 We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
L. Dupaigne, A. Farina
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Semilinear elliptic equations and fixed points [PDF]
Proceedings of the American Mathematical Society, 2004 In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $ \subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.
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Isolated boundary singularities of semilinear elliptic equations [PDF]
Calculus of Variations and Partial Differential Equations, 2010 Given a smooth domain $ \subset\RR^N$ such that $0 \in \partial $ and given a nonnegative smooth function $ $ on $\partial $, we study the behavior near 0 of positive solutions of $- u=u^q$ in $ $ such that $u = $ on $\partial \setminus\{0\}$. We prove that if $\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then $u(x)\leq C \abs{x}^{-\frac{2}{q-
Ponce, Augusto +2 more
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Semilinear elliptic equations and supercritical growth
Journal of Differential Equations, 1987 \textit{H. Brezis} and \textit{L. Nirenberg} have proved the existence of positive solutions of the problem \(\Delta \tilde u+\lambda \tilde u+\tilde u^ p=0\) in \(\Omega\) and \(\tilde u=0\) on \(\partial \Omega\) for \(p\leq p_ c=(n+2)/(n-2)\), when the embedding of \(H^ 1_ 0(\Omega)\) in \(L^{p+1}(\Omega)\) is continuous [Commun. Pure Appl. Math. 36,
Budd, C, Norbury, J
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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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