Asymptotic problems for differential equations with bounded $\Phi$-Laplacian

Abstract

In this paper we deal with the asymptotic problem \begin{equation*} \bigl(a(t)\Phi (x^{\prime })\bigr)^{\prime }+b(t)F(x)=0\,,\quad \lim_{t\rightarrow \infty }x^{\prime }(t)=0\,,\quad x(t)>0\mbox{ for large } t\,.\qquad (\ast ) \end{equation*} Motivated by searching for positive radially symmetric solutions in a fixed exterior domain in ${\mathbb{R}}^{N}$ for partial differential equations involving the curvature operator, the global positiveness and uniqueness of (*) is also considered.