Author : Nujud Alshehri

We consider a two point conjugate boundary value problem of the form y^” (t)=f(t,y(t),y^’ (t)),a≤t≤b ,y(a)=a_1 ,y(b)=a_2,where a<b ,f:[a,b]×R^2⟶R is continuous and a_1and a_2 are real. The method of upper and lower solutions, coupled with monotone methods, is useful if f is independent of y^’. If the conjugate conditions,y(a)=a_1,y(b)=a_2, are replaced by right focal conditions y(a)=a_1,y^’ (b)=a_2, then the method of upper and lower solutions, coupled with monotone methods, is useful in the case that f depends on y and on y^’. In this talk, we construct a boundary value problem of the form y^” (t)=f(t,y(t),y^’ (t)),a≤t≤b ,y(a)=a_1 ,y^’ (b)=g(y,y^’ ), which is equivalent to the original two point conjugate problem and obtain sufficient conditions on f and on g such that the method of upper and lower solutions, coupled with monotone methods, is useful.

Keywords: Forced Monotone Methods etc.

Article published in International Journal of Current Engineering and Technology, Vol.7, No.2 (April-2017)