Existence theorems for a nonlinear second-order distributional differential equation

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.