Results 11 to 20 of about 376,175 (295)
Semilinear Elliptic Equations and Fixed Points [PDF]
arXiv, 2003 In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $\Omega\subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two operators, an existence principle of strong solutions is proved.
Cleon S. Barroso
arxiv +3 more sources
Bubble towers for supercritical semilinear elliptic equations [PDF]
Journal of Functional Analysis, 2004 We construct positive solutions of the semilinear elliptic problem $ u+ u + u^p = 0$ with Dirichet boundary conditions, in a bounded smooth domain $ \subset \R^N$ $(N\geq 4)$, when the exponent $p$ is supercritical and close enough to $\frac{N+2}{N-2}$ and the parameter $ \in\R$ is small enough.
Yuxin Ge, Ruihua Jing, Frank Pacard
openalex +5 more sources
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
semanticscholar +1 more source
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
semanticscholar +1 more source
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 +2 more
openaire +7 more sources
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
doaj +1 more source
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
openaire +4 more sources
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
semanticscholar +1 more source
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
doaj +1 more source
A Concentration Phenomenon for Semilinear Elliptic Equations [PDF]
Archive for Rational Mechanics and Analysis, 2012 For a domain $ \subset\dR^N$ we consider the equation $ - u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $ $ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in $ as $n\to\infty ...
Andrzej Szulkin, Nils Ackermann
openaire +3 more sources