dorsal/arxiv
View SchemaNonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions
| Authors | Joseph Iaia, Henry Warchall |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9309001 |
| URL | https://arxiv.org/abs/patt-sol/9309001 |
Abstract
: We establish existence of an infinite family of exponentially-decaying non-radial $C^2$ solutions to the equation $\Delta u + f(u) = 0$ on $R^2$ for a large class of nonlinearities $f$. These solutions have the form $u(r,\theta )=e^{i m\theta }w(r)$, where $r$ and $\theta$ are polar coordinates, $m$ is an integer, and $w:[0,\infty ) \to R$ is exponentially decreasing far from the origin. We prove there is a solution with each prescribed number of nodes.
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"abstract": ": We establish existence of an infinite family of exponentially-decaying\nnon-radial $C^2$ solutions to the equation $\\Delta u + f(u) = 0$ on $R^2$ for a\nlarge class of nonlinearities $f$. These solutions have the form $u(r,\\theta\n)=e^{i m\\theta }w(r)$, where $r$ and $\\theta$ are polar coordinates, $m$ is an\ninteger, and $w:[0,\\infty ) \\to R$ is exponentially decreasing far from the\norigin. We prove there is a solution with each prescribed number of nodes.",
"arxiv_id": "patt-sol/9309001",
"authors": [
"Joseph Iaia",
"Henry Warchall"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Nonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions",
"url": "https://arxiv.org/abs/patt-sol/9309001"
},
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