Results 21 to 30 of about 376,175 (295)
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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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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On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 Assume that Ω is a regular domain in the complex plane ℂ, and A(z) is a symmetric 2×2 matrix with measurable entries, det A = 1, and such that 1/K|ξ|2 ≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|2, ξ ∈ ℝ2, 1 ≤ K < ∞. We study the blow-up problem for a model semilinear equation div (A(z)∇u) = eu in Ω and show that the well-known Liouville–Bieberbach function solves the problem ...
Gutlyanskii, V.Y. +2 more
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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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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 + K ( x ) e 2 u = 0 \Delta u + K(x){e^{2u}} = 0 in R n
Kuo-Shung Cheng, Tai-Chia Lin
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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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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 Singular Semilinear Elliptic Equations [PDF]
Journal of Mathematical Analysis and Applications, 1993 Abstract For the semilinear elliptic equation Δ u + p ( x ) u −γ = 0, x ∈ R n , n ≥ 3, γ > 0, we show via the barrier method the existence of a positive entire solution behaving like | x | 2 − n near ∞.
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A new proof of the boundedness results for stable solutions to semilinear elliptic equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$ for all $C^1$
X. Cabré
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An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds [PDF]
, 2021 Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined from the knowledge of the Dirichlet-to-Neumann map associated to the semilinear elliptic equation. This extends the
arxiv +1 more source