Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-04-01

Journal: COMPUTERS & MATHEMATICS WITH APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 69

Issue: 8

Page Number: 771-776

ISSN: 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.