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

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U2 - 10.1016/j.camwa.2015.02.020

DO - 10.1016/j.camwa.2015.02.020

M3 - Article

AN - SCOPUS:84933277175

VL - 69

SP - 771

EP - 776

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 8

ER -