The qualitative behavior of a second-order system with zero diagonal coefficient.
The authors investigate the qualitative behavior of solutions of the autonomous planar system \[ \dot{x}=p_2(y)\,q_2(x)\,y,\quad \dot{y}=p_3(y)\,q_3(x)\,x+p_4(y)\,q_4(x)\,y. \] Under suitable assumptions, necessary and sufficient conditions for all solutions to be oscillatory and for the origin to be a global center are established. Theorems on the existence and uniqueness of nontrivial periodic solutions are also proved.
scientific article; zbMATH DE number 2056515
scientific article