Fundamental solution of Sturm-Liouville equation

Picard's Theorem guarantees a unique solution of the ordinary differential equation (ODE) either systems of ODEs or the n-th order ODE. In this paper, it will be discussed the generalization of Picard's Theorem on Sturm-Liouville Equation with Lebesgue integrable function on [a, b]. Moreover, the solution of Sturm-Liouville Equation will be given in matrix form. Furthermore, it will be emphasized the relationship between the solution in matrix form and each entries on the matrix, as a solution on the generalization of Picard's Theorem. As a result, it will be discussed the fundamental solution of Sturm-Liouville Equation.