Results 41 to 50 of about 376,175 (295)
On a semilinear elliptic equation with inverse-square potential [PDF]
Selecta Mathematica, 2005 We study the existence and nonexistence of solutions to a semilinear elliptic equation with inverse-square potential. The dividing line with respect to existence or nonexistence is given by a critical exponent, which depends on the strength of the potential.
Alberto Tesei +3 more
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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
doaj +1 more source
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
semanticscholar +1 more source
On a semilinear elliptic equation in Hn
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009 We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
Gianni Mancini, K. Sandeep
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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-
Bidaut-Veron, Marie-Françoise +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
semanticscholar +1 more source
Semilinear elliptic equations on rough domains
Journal of Differential Equations, 2023 39 ...
Wolfgang Arendt, Daniel Daners
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A multiscale method for semilinear elliptic equations
Journal of Mathematical Analysis and Applications, 2008 AbstractAt present there are many papers, based on multiscale expansion and homogenization theory, to deal with nonlinear problems with microstructure. But there is no systematic method to deal with all of the possible nonlinear partial differential equations since different nonlinear problems gives rise to different multiscale expansions parameters ...
Yanping Lin +2 more
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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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On an inverse problem for a fractional semilinear elliptic equation involving a magnetic potential [PDF]
Journal of Differential Equations 296(2021) 170-185, 2020 We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. We determine the nonlinearity from the exterior partial measurements of the Dirichlet-to-Neumann map by using first order linearization and the Runge approximation property.
arxiv +1 more source