A new approximation scheme for first-order ordinary differential equations with non-negative right-hand sides Original Research Article

We prove an existence result for first-order ordinary differential equations subject to initial conditions. Assuming that the nonlinear part of the equation is nonnegative, among some other technical hypotheses, we construct a new approximation scheme by means of which we obtain the existence of solutions. Our main result ensures the solvability of a type of discontinuous differential equations that had not been previously considered.