Title: Existence theorems for a nonlinear second-order distributional differential equation,
Abstract: In this work, we are concerned with existence of solutions for a nonlinear
second-order distributional differential equation, which contains measure
differential equations and stochastic differential equations as special cases.
The proof is based on the Leray--Schauder nonlinear alternative and
Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to
demonstrate that the main results are sharp.