Non-local second-order boundary value problems with derivative-dependent nonlinearity

We prove the existence of multiple positive solutions nonlinear second-order nonlocal boundary value problems with term having derivative dependence. allow nonlinearity to grow quadratically respect derivatives. obtain a priori bounds for norms derivatives by using recently obtained Gronwall-type inequality. Three examples illustrate some results. This article is part theme issue ‘Topological degree and fixed point theories in differential difference equations’.