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

Z. Dosla, Masaryk University, Brno, Czech Republic
M. Cecchi, University of Florence, Firenze, Italy
M. Marini, University of Florence, Firenze, Italy

E. J. Qualitative Theory of Diff. Equ., Spec. Ed. I, 2009 No. 9., pp. 1-18.

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 ${\R}^{N}$ for partial differential equations involving the curvature operator, the global positiveness and uniqueness of
(*) is also considered.

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