Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case

Abstract

We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation \begin{equation*} u'' + c u' + λa(t) g(u) = 0, \end{equation*} where $g:[0,+\infty [\to [0,+\infty [$ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ${\int }_0^{T}a(t)dt<0$ and $\lambda >0$ is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

26 pages