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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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Rapid evaluation of radial basis functions [PDF]
, 2005 Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem.
Baxter, Brad J.C. +3 more
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Radial solutions for a Dirichlet problem in a ball
Journal of Differential Equations, 1985 Let \(\Omega \subset {\mathbb{R}}^ N\) be a bounded smooth domain. Let \(\lambda_ 1\) be the first eigenvalue of -\(\Delta\) on \(H^ 1_ 0(\Omega)\) and let \(\Phi_ 1>0\) be a corresponding eigenfunction. The Ambrosetti-Prodi problem \[ (1)\quad -\Delta u=f(x,u)+h(x)+t\Phi_ 1(x)\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] where \(t\in
Costa, D.G, de Figueiredo, D.G
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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 +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 +2 more
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Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients [PDF]
, 2012 This is the post-print version of the final paper published in Computers & Mathematics with Applications. The published article is available from the link below.
Škerget, L +7 more
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Radial solutions of a biharmonic equation with vanishing or singular radial potentials [PDF]
Nonlinear Analysis, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marino Badiale +2 more
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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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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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On radial solutions for Monge–Ampère equations
TURKISH JOURNAL OF MATHEMATICS, 2018 Summary: In this paper, we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampère equations using the fixed point theorem.
Ronghua LIU, Fanglei WANG, Yukun AN
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