非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0)

We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t)x+g(t, x,λ),0<t<1,x(0) = x(1) =x'(0)=x'(1)=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we sh...

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Bibliographic Details
Main Author: SHENWenguo(沈文国)
Format: Article
Language:zho
Published: Zhejiang University Press 2016-09-01
Series:Zhejiang Daxue xuebao. Lixue ban
Subjects:
Online Access:https://doi.org/10.3785/j.issn.1008-9497.2016.05.005
Description
Summary:We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t)x+g(t, x,λ),0<t<1,x(0) = x(1) =x'(0)=x'(1)=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we show that (λk,0) is a bifurcation point of the above problem. And there are two distinct unbounded continuas, and ,consisting of the bifurcation branch Ck from (λk,0),where λk is the k-th eigenvalue of the linear problem corresponding to the above problems. As an application of the above result,the global behavior of the components of nodal solutions of the following problem x"" + kx" +lx = rh(t) f(x) , 0<t<1, x(0)=x(1)=x'(0) = x'(1)=0 is studied. We obtain the existence of multiple nodal solutions for the problem if f0 =∞, f∞ ∈ (0,∞),.
ISSN:1008-9497