Existence And Multiplicity Of Positive Solutions To System Of Nonlinear Third-order Three-point BVPs

Third-order differential equations is widely used in various fields of Applied Mathematics and physics,for example,gravity driven flows,a three-layer beam,in the deflection of a curved beam having a constant or varying cross-section,electromagnetic waves,and so on.Therefore,multi-point boundary value problem of third-order differential equations has been widely concerned and achieved remarkable results.With the more extensive study on multi-point boundary value problem of third-order differential equations,the multi-point boundary value problem system of third-order differential equation is gradually becoming the research object.In this paper,we research the existence and multiplicity of positive solutions to system of the following nonlinear third-order three-point boundary value problems where 0<η≤?,0≤α<1,f,g∈C([0,1]×[0,∞),[0,∞))and for all t∈[0,1],f(t,0)≡0,g(t,0)≡0.The main tools used are the theory of the fixed-point index.