A new Chebyshev criterion and its application to planar differential systems

Abstract

This paper establishes a new Chebyshev criterion for a certain family of integrals. By virtue of this criterion we obtain several new Chebyshev families. With the help of these new families we can answer the problem proposed by Gasull et al. in 2015. Their applications to other two planar differential systems also show that our approach is simpler and in a unified way to handle some kinds of planar differential systems for estimating the number of limit cycles bifurcating from period annulus.