On resonant systems with rapidly rotating nonlinearities

P. AMSTER

Workshop; Nonlinear Analysis Workshop at the Claremont Center for the Mathematical Sciences; 2012

A second order resonant system of differential equations is studied. A well known result by Nirenberg establishes the existence of solutions if the nonlinearity is bounded and has uniform radial limits at infinity, provided that its degree over large balls is different from zero. In particular, the condition on existence of radial limits implies that the nonlinearity cannot rotate too fast. In contrast with Nirenberg's result, we shall allow rapid rotation and sublinear growth.