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Some remarks on singular solutions of nonlinear elliptic equations. I [PDF]
, 2009 The paper concerns singular solutions of nonlinear elliptic ...
Caffarelli, Luis +2 more
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Radially Symmetric Solutions of
International Journal of Differential Equations, 2012 We investigate solutions of and focus on the regime and . Our advance is to develop a technique to efficiently classify the behavior of solutions on , their maximal positive interval of existence.
William C. Troy, Edward P. Krisner
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On singular solutions of Lane-Emden equation on the Heisenberg group
Advanced Nonlinear Studies, 2023 By applying the gluing method, we construct infinitely many axial symmetric singular positive solutions to the Lane-Emden equation: ΔHu+up=0,inHn\{0}{\Delta }_{{\mathbb{H}}}u+{u}^{p}=0\left,\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0 ...
Wei Juncheng, Wu Ke
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Singular standing-ring solutions of nonlinear partial differential equations
, 2009 We present a general framework for constructing singular solutions of nonlinear evolution equations that become singular on a d-dimensional sphere, where d>1. The asymptotic profile and blowup rate of these solutions are the same as those of solutions of
Bricmont +30 more
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Singular solution to Special Lagrangian Equations
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 We prove the existence of non-smooth solutions to three-dimensional Special Lagrangian Equations in the non-convex case. Résumé Nous démontrons l'existence de solutions singulières d'équations speciales lagrangiennes en dimension trois, dans le cas non convexe.
Nadirashvili, Nikolai, Vlăduţ, Serge
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Solutions of singular integral equations
International Journal of Mathematics and Mathematical Sciences, 1982 Qualitative behavior of solutions of possibly singluar integral equations is studied. It includes properties such as positivity, boundedness and monotonicity of the solutions of the infinite interval.
Rina Ling
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Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity
Advanced Nonlinear Studies, 2020 Let Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} (N≥3{N\geq 3}) be a C2{C^{2}} bounded domain, and let δ be the distance to ∂Ω{\partial\Omega}. We study equations (E±){(E_{\pm})}, -Lμu±g(u,|∇u|)=0{-L_{\mu}u\pm g(u,\lvert\nabla u\rvert)=0} in Ω, where Lμ=Δ+μδ2 ...
Gkikas Konstantinos T., Nguyen Phuoc-Tai
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Twin Solutions to Singular Dirichlet Problems
Journal of Mathematical Analysis and Applications, 1999 The authors consider the Dirichlet second-order boundary value problem \[ y''+ \phi(t)[g(y(t))+ h(y(t))]= 0,\quad 0< t< 1,\quad y(0)= y(1)= 0,\tag{1} \] and establish the existence of two solutions \(y_1,y_2\in C[0,1]\cap C^2(0, 1)\) with \(y_1> 0\), \(y_2> 0\) on \((0,1)\). The nonlinearity in (1) may be singular at \(y= 0\), \(t= 0\) and/or \(t= 1\).
Agarwal, R.P., O'Regan, D.
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Singular solutions of fractional order conformal Laplacians
, 2011 We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe ...
Gonzalez, Maria del Mar +2 more
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Singular solutions to a quasilinear {ODE}
Advances in Differential Equations, 2005 7
DALBONO, Francesca +1 more
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