We give a structure result for the positive radial solutions of the following equation: $${\Delta }_{p}u+K\left(r\right)u{\left|u\right|}^{q-1}=0$$ with some monotonicity assumptions on the positive function $K\left(r\right)$. Here $r=\left|x\right|$, $x\in {ℝ}^n$; we consider the case when $n>p>1$, and $q>p_{*}=\frac{n(p-1)}{n-p}$. We continue the discussion started by Kawano et al. in [KYY], refining the estimates on the asymptotic behavior of Ground States with slow decay and we state the existence of S.G.S., giving also for them estimates on the asymptotic behavior, both as $r\to 0$ and as $r\to \infty$. We make use of a Emden-Fowler transform...

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields.Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators.Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0,1)$ vector fields satisfies...