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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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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Construction of Radial and Non-radial Solutions for Local and Non-local Equations of Liouville Type [PDF]
, 2021 This paper deals with radial and non-radial solutions for local and nonlocal Liouville type equations. At first non-degenerate and degenerate mean field equations are studied and radially symmetric solutions to the Dirichlet problem for them are written ...
Slavova, Angela, Popivanov, Petar
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Radial and non-radial solutions for a nonlinear Schrodinger equation with a constraint
Electronic Journal of Differential Equations, 2021 We study the classical nonlinear Schodinger equation with a radially symmetric potential and a constraint, for the mass subcritical case. We obtain conditions that assure the existence of non-radial solutions. Also we show symmetry breaking of the ground states, and the existence of multiple non-radial solutions under additional conditions. Folr ...
Jiaxuan Yang +2 more
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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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Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods [PDF]
, 2012 This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Taylor & Francis.This paper presents new formulations of the boundary–domain integral equation (BDIE) and the boundary–domain integro-
Al-Jawary, MA, Wrobel, LC
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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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The problem of dynamic cavitation in nonlinear elasticity [PDF]
, 2012 The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with polyconvex energy)
Miroshnikov, Alexey +5 more
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A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type [PDF]
, 2023 summary:We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$.
Bae, Soohyun
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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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