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论文类型：期刊论文

发表时间：2015-04-01

发表刊物：COMPUTERS & MATHEMATICS WITH APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：69

期号：8

页面范围：771-776

ISSN号：0898-1221

关键字：Global bifurcation; Kirchhoff type problem; Positive solution

摘要：In this paper, we study global bifurcation phenomena for the following Kirchhoff type problem
   {-M (integral(Omega) vertical bar del u(x)vertical bar(2) dx) Delta u = lambda f (x, u) in Omega,
   u = 0 on partial derivative Omega,
   where M is a continuous function. Under some natural hypotheses, we show that (lambda(1) (a)M(0), 0) is a bifurcation point and there is a global continuum e emanating from (lambda(1) (a)M(0), 0), where lambda(1) (a) denotes the first eigenvalue of the above problem with f (x, s) = a(x)s. As an application of the above result, we study the existence of positive solution for this problem with asymptotically linear nonlinearity. (C) 2015 Elsevier Ltd. All rights reserved.