Existence of solutions for first order singular problems

Abstract

We develop the lower and upper solutions method for first order initial value problems as well as for first order periodic problems in case the nonlinearity presents singularities. More precisely we prove that if we have a lower solution $\alpha$ and an upper solution $\beta$ of these problems, which are not necessarily continuous nor ordered, we have a solution wedged between $\min \{\alpha ,\beta \}$ and $\max \{\alpha ,\beta \}$.