Existence And Pathwise Uniqueness Of Solutions To Sturm-Liouville Problem For A Class Of Second Order Differential Equations With White Noise Perturbation

This paper concerns the second order stochastic differential equation on [0,1] with Sturm-Liouville boundary conditions We define the solutions in some whole measurable sense and give the definition of path-wise uniqueness. On the basis of nonlinear alternative theorem, we give some sufficient conditions for the existence and pathwise uniqueness of a solution assuming the Lips-chitz’s conditions on f.