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Construction of singular limits for a semilinear elliptic equation in dimension 2

✍ Scribed by Sami Baraket; Frank Pacard

Publisher
Springer
Year
1997
Tongue
English
Weight
387 KB
Volume
6
Category
Article
ISSN
0944-2669

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πŸ“œ SIMILAR VOLUMES

Solutions for a class of singular semili
Solutions for a class of singular semilinear elliptic equations
✍ Zhiren Jin πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 715 KB

~ eivcd 26 /"ehruatT /996. received tn rt 'vised lorm 13 ~larch 1996. re(ezv(.d l, r puhli('ation 27 Vov('mher 199Β’~) kΒ’.v w.rd,~ am/ phrase,: t!ntire solutions, semilinear elltptic equations, upper and lower solution method I. INTRODU('TI(.)N ANI) RI!SUI.TS = (1 + Ix'12) '+~Β°t w(x)-~ -> (1 + Ix']2)

Nonradial Solutions of a Semilinear Elli
Nonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions
✍ J. Iaia; H. Warchall πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 668 KB

We establish existence of an infinite family of exponentially-decaying non-radial \(C^{2}\) solutions to the equation \(\Delta u+f(u)=0\) on \(\mathbb{R}^{2}\) for a large class of nonlinearities \(f\). These solutions have the form \(u(r, \theta)=e^{\text {imit }} u(r)\), where \(r\) and \(\theta\)

Singularities for a 2-Dimensional Semili
Singularities for a 2-Dimensional Semilinear Elliptic Equation with a Non-Lipschitz Nonlinearity
✍ Marie-Francoise Bidaut-VΓ©ron; Victor Galaktionov; Philippe Grillot; Laurent VΓ©ro πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 186 KB

We study the limit behaviour of solutions of the semilinear elliptic equation with a non-Lipschitz nonlinearity on the right-hand side. When |\_+2| 2 we give a complete classification of the types of singularities as x Γ„ 0 and x Γ„ which in the rescaled form are essentially non-analytic and, even mo