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论文类型：期刊论文

发表时间：2016-09-01

发表刊物：TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS

收录刊物：SCIE、Scopus

卷号：48

期号：1

页面范围：213-233

ISSN号：1230-3429

关键字：Bifurcation; eigenvalue; Kirchhoff type equation; positive solutions

摘要：In this paper, we shall study global bifurcation phenomenon for the following Kirchhoff type problem:
   {-(a + b integral(Omega) vertical bar del(u)vertical bar(2) dx) Delta u = lambda u + h(x, u, lambda) in Omega,
   u = 0 on Omega.
   Under some natural hypotheses on h, we show that (a lambda(1), 0) is a bifurcation point of the above problem. As an application of the above result, we shall determine the interval of lambda, in which there exist positive solutions for the above problem with h(x, u; lambda) = lambda f (x, u) - lambda u, where f is asymptotically linear at zero and asymptotically 3-linear at infinity. To study global structure of bifurcation branch, we also establish some properties of the first eigenvalue for a nonlocal eigenvalue problem. Moreover, we provide a positive answer to an open problem involving the case a = 0.