TY - JOUR
T1 - Global bifurcation and positive solution for a class of fully nonlinear problems
AU - Dai, Guowei
AU - Wang, Haiyan
AU - Yang, Bianxia
N1 - Funding Information:
Research supported by NNSF of China (Nos. 11261052 , 11401477 ), the Fundamental Research Funds for the Central Universities (No. DUT15RC(3)018 ) and Scientific Research Project of the Higher Education Institutions of Gansu Province (No. 2014A-009).
Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.
PY - 2015
Y1 - 2015
N2 - In this paper, we study global bifurcation phenomena for the following Kirchhoff type problem {-M (/ Ω/ ∇u(x)|2 dx) Δu = λf (x, u) in Ω, u = 0 on ∂Ω, where M is a continuous function. Under some natural hypotheses, we show that (λ1(a)M(0), 0) is a bifurcation point and there is a global continuum C emanating from (λ1(a)M(0), 0), where λ1(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.
AB - In this paper, we study global bifurcation phenomena for the following Kirchhoff type problem {-M (/ Ω/ ∇u(x)|2 dx) Δu = λf (x, u) in Ω, u = 0 on ∂Ω, where M is a continuous function. Under some natural hypotheses, we show that (λ1(a)M(0), 0) is a bifurcation point and there is a global continuum C emanating from (λ1(a)M(0), 0), where λ1(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.
KW - Global bifurcation
KW - Kirchhoff type problem
KW - Positive solution
UR - http://www.scopus.com/inward/record.url?scp=84933277175&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84933277175&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2015.02.020
DO - 10.1016/j.camwa.2015.02.020
M3 - Article
AN - SCOPUS:84933277175
SN - 0898-1221
VL - 69
SP - 771
EP - 776
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 8
ER -