Remarks on the periodic boundary value problems for first-order differential equations
The authors apply the method of upper and lower solutions and the monotone iterative technique to the first-order periodic boundary value problem \(u'(t)=f(t,u(t))\), \(t\in I=[0,2\pi]\); \(u(0)=u(2\pi)\), where \(f:I\times \mathbb{R}\to \mathbb{R}\) is a continuous function. They investigate the case when the classical inequalities for the boundary conditions are violated in the definitions of the upper and lower solutions. Some examples are included showing the applicability of the main results and the necessity of requiring new hypotheses on the nonlinearity \(f\).
scientific article; zbMATH DE number 1357964