Bifurcations from infinity in asymmetric nonlinear oscillators
The authors study the existence of large-amplitude periodic and almost-periodic solutions to second-order differential equations with asymmetric nonlinearities of the following type \[ x^{\prime \prime }+\mu x^{+}-\upsilon x^{-}=g(t,x,x',\varepsilon) \] with \(\mu >0,\) \(\upsilon >0,\quad \frac{1}{\sqrt{ \mu }}+\frac{1}{\sqrt{\upsilon }}=\frac{2}{n}\) for some positive \(n\), and \(\varepsilon \) is a small parameter. The pair \(\left( \mu ,\upsilon \right) \) belongs to the \(n\)th-Fucik spectrum. The authors call this situation nonlinear resonance. They consider the problem of bifurcation from infinity when \(\varepsilon \) is near zero. The paper is well organized and the results are very interesting.
large-amplitude periodic and almost-periodic solutions
scientific article; zbMATH DE number 1439281
scientific article