We prove the existence of positive radial solutions of the following equation: egin{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 egin{equation*} Delta_{m}u+K^1(r) u|u|^{q-2}+K^2(r) u|u|^{p-2}=0 end{equation*} when $q
M. FRANCA (2005). Some results on the m-Laplace equations with two growth terms. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 17(2), 391-425 [10.1007/s10884-005-4572-5].
Some results on the m-Laplace equations with two growth terms
M. FRANCA
Membro del Collaboration Group
2005
Abstract
We prove the existence of positive radial solutions of the following equation: egin{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 egin{equation*} Delta_{m}u+K^1(r) u|u|^{q-2}+K^2(r) u|u|^{p-2}=0 end{equation*} when $qI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
