On a resonant elliptic system with rapidly rotating nonlinearities

P. AMSTER

Rio de Janeiro

Seminario; PDEs Seminar; 2016

IMPA

A second order system of elliptic partial differential equations under Neumann conditions 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 topological 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.