Resonant forced oscillations in systems with periodic nonlinearities (Q1943270)

The author studies the set of \(2\pi\)-periodic solutions for an ordinary differential equation of the type \[ L(p)x=f(x)+b(t),\quad p=d/dt, \] where \(L\) is a polynomial with constant coefficients and degree at least \(2\), \(f:\mathbb R\to\mathbb R\) is continuous and periodic with a period \(T\), and \(b:\mathbb R\to\mathbb R\) is continuous and \(2\pi\)-periodic. Existence and multiplicity results are obtained, even in the resonant case.