Radial solutions with a vortex to an asymptotically linear elliptic equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Radial solutions with a vortex to an asymptotically linear elliptic equation

Authors:

Tatsuya Watanabe

Affiliation:

(1) Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Abstract:

In this paper, we study a two-dimensional nonlinear elliptic equation:

$-Delta v(x) + V (x)v(x) = f(v(x)), x in {mathbb{R}}^{2}$

where V (x) is radial, V (x) behaves like $O left( frac{1}{|x|}^2 right)$ near zero and the nonlinearity f is asymptotically linear at infinity. We show the existence of a nontrivial radial solution of (1.1) via the variational approach. Supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists

Keywords:

KeywordHeading" >. asymptotically linear nonlinearity vortex variational method

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