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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A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth [PDF]
, 2017 Yasuhito Miyamoto
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Concentration and dynamic system of solutions for semilinear elliptic equations
Electronic Journal of Differential Equations, 2003 In this article, we use the concentration of solutions of the semilinear elliptic equations in axially symmetric bounded domains to prove that the equation has three positive solutions. One solution is y-symmetric and the other are non-axially symmetric.
Tsung-fang Wu
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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.
G. Catino, D. Monticelli
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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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Bifurcations for semilinear elliptic equations with convex nonlinearity
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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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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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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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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