Results 11 to 20 of about 75,181 (273)

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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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, E. Vecchi, S. Dipierro, E. Valdinoci   +3 more
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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, Pei Ma, Xiaohuan Wang, Hongyi Li   +3 more
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Solutions of Semilinear Elliptic Equations in Tubes [PDF]

Journal of Geometric Analysis, 2012
Given a smooth compact k-dimensional manifold embedded in $\mathbb {R}^m$, with m\geq 2 and 1\leq k\leq m-1, and given >0, we define B_ ( ) to be the geodesic tubular neighborhood of radius about . In this paper, we construct positive solutions of the semilinear elliptic equation u + u^p = 0 in B_ ( ) with u = 0 on \partial B_ ...
Frank Pacard, PACELLA, Filomena, Sciunzi Berardino   +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
Kuo-Shung Cheng, Tai-Chia Lin
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A two-grid $ P_0^2 $-$ P_1 $ mixed finite element scheme for semilinear elliptic optimal control problems

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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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, A. Figalli, Xavier Ros-Oton, J. Serra   +3 more
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