Some results on the m-Laplace equations with two growth terms

We prove the existence of positive radial solutions of the following equation: \begin{equation*} \Delta_{m}u-K^1(r) u|u|^{q-2}+K^2(r) u|u|^{p-2}=0 \end{equation*} and give sufficient conditions on the positive functions $K^1(r)$ and $K^2(r)$ for the existence and nonexistence of G.S. and S.G.S., when $q< m^* \le p$ or $q=m^* < p$. We also give sufficient conditions for the existence of radial S.G.S. and G.S. of equation \begin{equation*} \Delta_{m}u+K^1(r) u|u|^{q-2}+K^2(r) u|u|^{p-2}=0 \end{equation*} when $q<p \le m^* $ and $m^* \le q <p $ respectively. We re also able to classify all the S.G.S. of this equation. The proofs use a new Emden-Fowler transform which allow us to use techniques taken from dynamical system theory, in particular the ones developed in \cite{JPY2} for the problems obtained by substituting the ordinary Laplacian $\Delta$ for the $m$-Laplacian $\Delta_{m}$ in the preceding equations.