Abstract
In this paper, the existence results of positive solutions for three-point Riemann-Stieltjes integral BVPs (boundary value problems) is considered. By applying shooting method and comparison principle, we obtain some new results which extend the known ones. At the same time, the theorems in one of our published articles are corrected by another theorem in this paper.
Highlights
1 Introduction By applying the shooting method, we establish the criteria for the existence of positive solutions to the following Riemann-Stieltjes integral BVPs: u (t) + a(t)f u(t) =, < t
We present the result for BVP ( . ) with ( . ), which is the correction of Theorem . and Theorem . in [ ]
The idea of this paper was illuminated by [, ]; the certain constant Lθ could not be given explicitly in [ ] and η only equals / in [ ]. From this point of view, this paper extends the work of [, ] and presents another way to find the ‘eigenvalue’ by numerical calculation, though it is related to a transcendental equation which has at least one numerical solution
Summary
Introduction By applying the shooting method, we establish the criteria for the existence of positive solutions to the following Riemann-Stieltjes integral BVPs: u (t) + a(t)f u(t) = , < t < , ) has at least one positive solution if one of the following conditions holds: (i) (ii) The sufficient condition for the existence of positive solutions is the super-linear case or the sub-linear case.
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