  The paper is devoted to the study of two-parametric families of Dirichlet
problems for systems of equations with $p, q$-Laplacians and indefinite
nonlinearities. Continuous and monotone curves $\Gamma_f$ and $\Gamma_e$ on the
parametric plane $\lambda \times \mu$, which are the lower and upper bounds for
a maximal domain of existence of weak positive solutions are introduced. The
curve $\Gamma_f$ is obtained by developing our previous work
\cite{BobkovIlyasov} and it determines a maximal domain of the applicability of
the Nehari manifold and fibering methods. The curve $\Gamma_e$ is derived
explicitly via minimax variational principle of the extended functional method.
