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J. Korean Math. Soc. 2002; 39(3): 439-460

Printed May 1, 2002

Copyright © The Korean Mathematical Society.

Existence of the third positive radial solution of a semilinear elliptic problem on an unbounded domain

Bong Soo Ko and Yong-Hoon Lee

Cheju National University and Pusan National University

Abstract

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We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

Keywords: existence, multiplicity, semilinear elliptic problem, singular boundary value problem, upper solution, lower solution, Leray-Schauder degree, radial solution

MSC numbers: 34B15, 35J25

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