On existence of infinitely many homoclinic solutions
Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation \[ \dot z=\bar z(1+\text{e}^{i\varepsilon t}|z|^2),\quad z\in\mathbb{C} . \]
scientific article; zbMATH DE number 1486214