Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations
The authors consider the differential equation \[ x^{m} \dot{x}=\sum_{k=0}^{n} a_{k}(t)x^{k}, \] where \(a_{k}\) are continuous \(T\)-periodic functions and \(m\) is a non-negative integer. It is assumed also that \(a_{0}(t)\) has at least one zero in the interval \((0,T)\). It is shown that the equation has a \(T\)-periodic solution which has the sign of \((-1)^{m}a_{0}(t)\) if some conditions on the other coefficients are satisfied.
scientific article; zbMATH DE number 6157269