Periodic positive solutions of superlinear delay equations via topological degree

Abstract

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 for g and sign alternance for a . 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’.