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Indexed by:期刊论文

Date of Publication:2015-04-01

Journal:COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:69

Issue:8

Page Number:771-776

ISSN No.:0898-1221

Key Words:Global bifurcation; Kirchhoff type problem; Positive solution

Abstract: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.