The effect of domain shape on the number of positive and nodal solutions for semilinear elliptic equations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

The effect of domain shape on the number of positive and nodal solutions for semilinear elliptic equations

Authors:	Tsung-fang Wu

Affiliation:	Department of Applied Mathematics, National University of Kaohsiung, No. 700, Kaohsiung University Road, Nantzu District, Kaohsiung 811, Taiwan

Abstract:	In this paper, we study the effect of domain shape on the number of positive and nodal (sign-changing) solutions for a class of semilinear elliptic equations. We prove a semilinear elliptic equation in a domain Ω $Ω$ that contains m $m$ disjoint large enough balls has m² $m^{2}$ 2-nodal solutions and m $m$ positive solutions.

Keywords:	Semilinear elliptic equations Positive solutions Nodal solutions
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