Elliptic Hamilton-Jacobi systems and Lane-Emden Hardy-H{é}non equations

Marie-Françoise Bidaut-Véron, Marta Garcia Huidobro

Here we study the solutions of any sign of the system --$\Delta$u 1 = |$\nabla$u 2 | p , --$\Delta$u 2 = |$\nabla$u 1 | q , in a domain of R N , N 3 and p, q > 0, pq > 1.. We show their rela…