Results 11 to 20 of about 35,706 (291)

Structure of Positive Radial Solutions of Semilinear Elliptic Equations

Journal of Differential Equations, 1997
This article primarily concerns uniqueness and asymptotic behavior of positive radial solutions to the semilinear problems (1) \(-\Delta u=f(u)\) in \(\mathbb{R}^n\), \(u(\infty)=0\); and (2) \(-\Delta u=f(u)\) in \(B\), \(u|_{\partial B}=0\), where \(B\) denotes a ball in \(\mathbb{R}^n\) centred at the origin, and \(f(t)= \min\{t^p,t^q\}\) for ...
Erbe, Lynn, Tang, Moxun
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Positive radial solutions involving nonlinearities with zeros [PDF]

Discrete and Continuous Dynamical Systems, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Isabel Flores, Matteo Franca, Leonelo Iturriaga   +2 more
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Radial Symmetry of Positive Solutions of Nonlinear Elliptic Equations

Journal of Differential Equations, 1999
Three results concerning the radial symmetry and asymptotic behaviour at \(x=\infty\) of positive solutions of \[ \Delta u = \varphi(\mid x\mid)u^{\lambda}, \quad x\in \mathbb{R}^n \] and \(|x|\) large are presented. Here \(\lambda>1\) and \(\varphi(r)\) is positive and continuous for \(r\) large. There are three cases which are separately analysed: (I)
Taliaferro, Steven D., Steven D. Taliaferro   +1 more
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Three positive radial solutions for elliptic equations in a ball

Applied Mathematics Letters, 2005
The authors consider the second-order elliptic problem of the form \[ -\Delta u=\lambda\cdot k(|x|) f(u),\quad u> 0\quad\text{in }\Omega,\quad u= a\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is the ball of radius \(R_0\); \(\lambda\), \(a\) are positive parameters; \(f\in C([0,+\infty), [0,+\infty))\) is a increasing function and \(k\in C(
João Marcos do Ó, Sebastián Lorca, Pedro Ubilla   +2 more
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Morse index and uniqueness for positive solutions of radial $p$-Laplace equations [PDF]

Transactions of the American Mathematical Society, 2004
The authors consider positive radial solutions to a radial \(p\)-Laplace equation on the unit ball with Dirichlet boundary conditions. Using the spectrum of the linearized operator in a weighted space of radial functions, they derive the Morse index and use it to prove uniqueness and nondegeneracy in some particular cases.
A. Aftalion, PACELLA, Filomena
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Radial Symmetry for Weak Positive Solutions of Fractional Laplacian with a Singular Nonlinearity [PDF]

Symmetry, 2018
This paper is concerned with the radial symmetry weak positive solutions for a class of singular fractional Laplacian. The main results in the paper demonstrate the existence and multiplicity of radial symmetry weak positive solutions by Schwarz spherical rearrangement, constrained minimization, and Ekeland’s variational principle. It is worth pointing
Xing Wang 0008, Li Zhang
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Existence of positive radial solutions for a weakly coupled system via blow up [PDF]

Abstract and Applied Analysis, 1998
The existence of positive solutions to certain systems of ordinary differential equations is studied. Particular forms of these systems are satisfied by radial solutions of associated partial differential equations.
Marta García-Huidobro, Ignacio Guerra, Raúl Manásevich   +2 more
doaj   +2 more sources

Positive Radial Symmetric Solutions of Nonlinear Biharmonic Equations in an Annulus

Symmetry
This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵2u=f(u,▵u) on an annular domain Ω in RN with the Navier boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:R+×R−→R+ is a continuous function.
Yongxiang Li, Shengbin Yang
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Multiplicity and symmetry breaking for positive radial solutions of semilinear elliptic equations modelling MEMS on annular domains

Electronic Journal of Differential Equations, 2005
The use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical system (MEMS) and in nanoelectromechanical systems (NEMS).
Peng Feng, Zhengfang Zhou
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S-shaped connected component of radial positive solutions for a prescribed mean curvature problem in an annular domain

Open Mathematics, 2019
In this paper, we show the existence of an S-shaped connected component in the set of radial positive solutions of boundary value ...
Xu Man, Ma Ruyun
doaj   +2 more sources