Research Of Positive Solutions To Boundary Value Problems For Three-order Nonlinear Differential Equations Of Two Kinds

In this paper, two categories of the third order nonlinear boundary value problems are discussed deeply, and some decent results are obtained.Firstly, we study the existence of positive solution for the third order three-point boundary value problem um(t)+h(t)f(t,u(t))=0,t∈(0,1),u(0)=u’(0)=0,u’(1)=α(η) by using generalize the fixed point theorem of Leggett-Williams. Where1<α<1/η,0<η<1and h(t) is allowed to be singular at t=0or t=1.Next, we study the existence of positive solution for the three order with integrals boundary value problem where λ>0is a constant, a:(0,1)â†'[0,+∞) is a continual function, a(t) is allowed to be singular at t=0or t=1,f:(0,1)x[0,+∞)x[0,+∞)â†'[0,+∞) is continues. By using functional fixed point theorem of expansion and compression in cone, an explicit interval for λ is derived such that for any A, in this interval, the existence of at least one positive solution to the above singular boundary value problem is guaranteed.