Periodic positive solutions of superlinear delay equations via topological degree

We extend to delay equations recent results obtained by G. Feltrin and F. Zanolin for second-order ordinary equations with a superlinear term. We prove the existence of positive periodic solutions for nonlinear delay equations −u ″(t ) = a (t )g (u (t ),u (t  − τ )). We assume superlinear growth forg and sign alternance fora . The approach is topological and based on Mawhin’s coincidence degree.This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.