Generalized quasilinearization and first-order periodic boundary value problem (Q1918302)

The periodic boundary value problem \(x' = f(t,x)\), \(x(0) = x(2\pi)\) is studied where \(f = F + G + h\), \(F(t,x) + \varphi(t,x)\) is convex for some convex function \(\varphi\), \(G(t,x) + \psi(t,x)\) is concave for some concave function \(\psi\) and \(h\) is Lipschitzian. This problem is solved by generalized quasilinearization which yields both-sided bounds with quadratic rate of convergence.