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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1998; 35(2): 387-398

Printed June 1, 1998

Copyright © The Korean Mathematical Society.

Nodal solutions of nonlinear elliptic equations in annular domains

Soon Yeun Jang and Dae Hyeon Pahk

Yonsei University and Yonsei University

Abstract

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We investigate the existence of radial nodal solutions of the elliptic equation $\triangle u +h(|x|)f(u)=0$, in annular domains. It is proved that for each integer $k \ge 1$, there exist at least one radially symmetric solution which has exactly $k$ nodes.

Keywords: radial solutions, nodes, shooting methods, annular domain

MSC numbers: 35B05, 35J60

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