Results 1 to 10 of about 77,874 (311)

On Radial Solutions of the Schrödinger Type Equation

Advanced Nonlinear Studies, 2011
Abstract We establish compact embeddings of the radial Sobolev space H rad 1,p (ℝ N ) into weighted Lebesgue spaces L q w (ℝ N
Chabrowski, Jan H., Grotowski, Joseph F.
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Uniqueness of Radial Solutions for the Fractional Laplacian [PDF]

Communications on Pure and Applied Mathematics, 2015
AbstractWe prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (−Δ)s with s ∊ (0,1) for any space dimensions N ≥ 1. By extending a monotonicity formula found by Cabré and Sire , we show that the linear equation urn:x-wiley:00103640:media:cpa21591:cpa21591-math-0001 has at most one
Frank, Rupert L., Lenzmann, Enno, Silvestre, Luis   +2 more
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Existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations

Nonlinear Analysis, 2018
In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball.
Jianxin He, Xinguang Zhang, Lishan Liu, Yonghong Wu   +3 more
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Glueballs—a radial solution?

Physics Letters B, 1983
Abstract We analyze the mass spectrum and radiative decays of the low lying pseudoscalar and vector mesons in a nonrelativistic model. We investigate the mixing of the gluonium candidate ι(1440) with the J PC = 0 −+ quarkonium candidates. The light quark content of these states as well as implications of the mixing is discussed.
Mariana Frank, Patrick J. O'Donnell
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Radially Symmetric Solutions of a Nonlinear Elliptic Equation [PDF]

International Journal of Mathematics and Mathematical Sciences, 2011
We investigate the existence and asymptotic behavior of positive, radially symmetric singular solutions of w′′ + ((N − 1)/r)w′−|w|p−1w = 0, r > 0. We focus on the parameter regime N > 2 and 1 < p < N/(N − 2) where the equation has the closed form, positive singular solution w1 = (4 − 2(N − 2)(p − 1)/(p − 1) 2) 1/(p−1)r−2/(p−1), r > 0 ...
Edward P. Krisner, William C. Troy
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Remarks on the uniqueness of radial solutions [PDF]

ESAIM: Mathematical Modelling and Numerical Analysis, 1989
Uniqueness of radial solutions for the problem \(\Delta u+f(u)=0\) in \(D=B_ R(0)\), with \(au-b(\partial u/\partial n)=0\) on \(\partial D\) is considered. Here a and b are constants and n denotes the outward normal unit vector. As usual, the problem is reduced to a second order ordinary differential equation for the radial solution u(r), \(r=| x|\), \
Smoller, J., Wasserman, A.
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Nonexistence of positive radial solutions for a problem with singular potential

Advances in Nonlinear Analysis, 2014
This article completes the picture in the study of positive radial solutions in the function space 𝒟1,2(ℝN)∩L2(ℝN,|x|-αdx)∩Lp(ℝN)${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the ...
Catrina Florin
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Branches of Radial Solutions for Semipositone Problems

Journal of Differential Equations, 1995
Let \(\Omega\) be the unit ball in \(\mathbb{R}^N\) \((N> 1)\) centered at the origin, \(f: \mathbb{R}\to \mathbb{R}\) a differentiable, monotone function such that \(f(0)< 0\), \(\lim_{d\to \infty} {f(x)\over d}= \infty\), \(F(d)- {N- 2\over 2N} df(d)\geq M\) for all \(d\in \mathbb{R}\), where \(M\in \mathbb{R}\), \(F(d)= \int^d_0 f(s) ds\) and ...
Castro, Alfonso, Gadam, Sudhasree, Shivaji, R.   +2 more
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Radial solutions to the wave equation [PDF]

Annali di Matematica Pura ed Applicata, 2002
The authors study the Cauchy problem \[ \begin{gathered} \frac{\partial^2u}{\partial t^2}(t,x) =\frac{\partial^2u}{\partial x^2}(t,x) +\frac{2\alpha+1}{x}\frac{\partial u}{\partial x}(t,x),\\ u(0,x)=\phi(x),\,\,\,\frac{\partial u}{\partial x}(0,x)=\psi(x), \end{gathered} \] where \(\alpha\geq -1/2\) and ...
COLZANI, LEONARDO, Cominardi, A, Stempak, K.   +2 more
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A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations

Mathematics, 2020
In this article, a novel radial−based meshfree approach for solving nonhomogeneous partial differential equations is proposed. Stemming from the radial basis function collocation method, the novel meshfree approach is formulated by incorporating ...
Cheng-Yu Ku, Jing-En Xiao, Chih-Yu Liu
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