The existence of solutions to second-order singular boundary value problems

This article analyzes qualitative properties of solutions to two-point boundary value problems for singular ordinary differential equations. In particular, we form new approaches that ensure that all possible solutions satisfy certain a priori bounds. The methods involve differential inequalities.The ideas are then applied to generate new existence results for solutions to the boundary value problems under consideration. Many of the results are novel for both the singular and the nonsingular cases.The main concepts are further illustrated via applications to various equations arising in modeling, such as the Poisson–Boltzmann equation, and the Thomas–Fermi equation with an ionized atom.