Daniel R. Baker, Reducing Nonlinear Systems of Transport Equations to Laplace's Equation, SIAM Journal on Applied Mathematics, Vol. 53, No. 2 (Apr., 1993), pp. 419-439 ...

A class of linear integrodifferential equations in general Banach space is studied by means of Laplace transform methods. The results are applied to the nonlinear case to get results on existence in ...

There are many applications for the Laplace transform, including transforming types of differential equations.