Abstract:

Using the method of upper and lower solutions, in the sense of generalized derivative, we studied the existence of solutions of the second order nonlinear boundary value problems involving the distributional HenstockKurzweil integral. First, we introduced the definition and nature of the distributional Henstock-Kurzweil integral. Then, by the method of upper and lower solutions, we got the conclusion that operator A is progressively increase and relatively compact through three steps. Finally, we demonstrated through examples that the solutions of this kind of problem exist.

Key words: distributional HenstockKurzweil integral, the second order nonlinear boundary value problems, distributional derivative, upper and lower solutions