Results 11 to 20 of about 93,033 (295)
Semilinear fractional elliptic equations involving measures [PDF]
Journal of Differential Equations, 2013 We study the existence of weak solutions of (E) $ (-\Delta)^\alpha u+g(u)=\nu $ in a bounded regular domain $\Omega$ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus\Omega$, where $(-\Delta)^\alpha$ denotes the fractional Laplacian with $\alpha\in(0,1)$,
Chen, Huyuan, Veron, Laurent
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Isolated singularity for semilinear elliptic equations
Discrete & Continuous Dynamical Systems - A, 2015 In this paper, we study a class of semilinear elliptic equations with the Hardy potential. By means of the super-subsolution method and the comparison principle, we explore the existence of a minimal positive solution and a maximal positive solution.
Lei Wei, Zhaosheng Feng
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Entire solutions of semilinear elliptic equations
Electronic Journal of Differential Equations, 2004 We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors.
Alexander Gladkov, Nickolai Slepchenkov
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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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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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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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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 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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Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent
AIMS Mathematics, 2021 This paper is devoted to study a class of semilinear elliptic equations with variable exponent. By means of perturbation technique, variational methods and a priori estimation, the existence of infinitely many sign-changing solutions to this class of ...
Changmu Chu, Yuxia Xiao , Yanling Xie
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