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Solutions of Laplace's equation in two dimensions with a curved longitudinal axis

✍ Scribed by S.R. Mane

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
797 KB
Volume
321
Category
Article
ISSN
0168-9002

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πŸ“œ SIMILAR VOLUMES

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 \(\theta\)