Results 11 to 20 of about 92,595 (298)
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature [PDF]
Journal of the European Mathematical Society (Print), 2022 In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature.
Giovanni Catino, Dario D. Monticelli
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Boundedness of stable solutions to semilinear elliptic equations: a survey [PDF]
, 2017 This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known $L^{\infty}$ estimates that hold for all nonlinearities.
Brown, André EX (5398142) +11 more
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Semilinear elliptic equations involving mixed local and nonlocal operators [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020 In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on
Stefano Biagi +3 more
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Bifurcations for semilinear elliptic equations with convex nonlinearity [PDF]
Electronic Journal of Differential Equations, 1999 We investigate the exact number of positive solutions of the semilinear Dirichlet boundary value problem $Delta u+f(u) = 0$ on a ball in ${mathbb R}^n$ where $f$ is a strictly convex $C^2$ function on $[0,infty)$. For the one-dimensional case we classify
J. Karatson, Peter L. Simon
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Regularity and Symmetry for Semilinear Elliptic Equations in Bounded Domains [PDF]
Communications in Contemporary Mathematics, 2021 In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations. We shall focus on the following class : Definition 1. Let N ≥ 1, Ω ⊂ R denote an open set and f ∈ C(R).
L. Dupaigne, A. Farina
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Singular solutions for semilinear elliptic equations with general supercritical growth
Annali di Matematica Pura ed Applicata, 2022 A positive radial singular solution for $$\Delta u+f(u)=0$$ Δ u + f ( u ) = 0 with a general supercritical growth is constructed. An exact asymptotic expansion as well as its uniqueness in the space of radial functions are also established. These results
Yasuhito Miyamoto, Y. Naito
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Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities [PDF]
Calculus of Variations and Partial Differential Equations, 2020 We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and derivatives of the Dirichlet-to-Neumann map hold.
Yi-Hsuan Lin
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Nondegeneracy of the bubble solutions for critical equations involving the polyharmonic operator
Boundary Value Problems, 2023 We reprove a result by Bartsch, Weth, and Willem (Calc. Var. Partial Differ. Equ. 18(3):253–268, 2003) concerning the nondegeneracy of bubble solutions for a critical semilinear elliptic equation involving the polyharmonic operator.
Dandan Yang +3 more
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On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 This paper deals with the blow-up problem for a model semilinear equation of the type \[ \text{div}(A(z)\nabla u)= e^u \] in a simply connected domain \(\Omega\subset \mathbb{C}^1\). \(A(z)\) is a \(2\times 2\) symmetric uniformly elliptic matrix with measurable entries and \(\text{det\,}A=1\).
Gutlyanskii, V.Y. +2 more
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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
Cheng, Kuo-Shung, Lin, Tai-Chia
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