Existence of Entire Solutions of a Singular Semilinear Elliptic Problem

Authors: Feng, Wei¹; Liu, Xi²

Source: Acta Mathematica Sinica, Volume 20, Number 6, November 2004 , pp. 983-988(6)

Publisher: Springer

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Abstract:

In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang's paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems.

Keywords: Singular semilinear elliptic problem; Sobolev embedding theorems; Maximum principle; 34J25

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-004-0391-6

Affiliations: 1: Department of Mathematics, Beijing University of Aeronautics and Astronautics, LIMB of the Ministry of Education, Beijing 100083, P. R. China, Email: fengwj75@126.com 2: School of Information and Mangement, Shandong Normal University, Jinan 250014, P. R. China, Email: yliu@jn-public.sd.cninfo.net

Publication date: 2004-11-01