Abstract: The positive solutions were considered for a class of nonlinear third-order ordinary differential equations, where the nonlinear term contains first derivative of unknown function and may be singular in the term variable. The main conditions of the results are local. In other words, the equation may have 1-3 positive solutions provided the integrations of height functions of nonlinear term on some bounded sets are appropriate.

Key words: boundary value problem, positive solution, existence, multiplicity, singular ordinary differential equation, boundary value problem, positive solution, existence, multiplicity