Problems at resonance for equations with periodic nonlinearities Original Research Article

We study differential equations with periodic nonlinearities. In particular, we prove that for |a| small, the equation View the MathML source, where g is a C1 periodic function with zero mean value and h is orthogonal to View the MathML source and View the MathML source, has 2π-periodic solutions. The proof relies on an abstract result based on variational arguments; its application makes use of integral estimates by the stationary phase method. We also study the existence of multiple solutions.