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论文类型：期刊论文

发表时间：2018-11-05

发表刊物：ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

收录刊物：SCIE、Scopus

卷号：2018

ISSN号：1072-6691

关键字：Bifurcation; spectrum; nonlocal problem; nodal solution

摘要：In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type problem
   -(a+b integral(1)(0) vertical bar u'vertical bar(2) dx)u '' =lambda u+h(x,u,lambda) in (0,1),
   u(0) = u(1) = 0.
   Under natural hypotheses on h, we show that (a lambda(k), 0) is a bifurcation point of the above problem. As applications we determine the interval of lambda, in which there exist nodal solutions for the Kirchhoff-type problem
   -(a+b integral(1)(0) vertical bar u'vertical bar(2) dx)u '' =lambda f(x,u) in (0,1),
   u(0) = u(1) = 0.
   where f is asymptotically linear at zero and is asymptotically 3-linear at infinity. To do this, we also establish a complete characterization of the spectrum of a nonlocal eigenvalue problem.