E-mail: matucci@math.unifi.it
Abstract. The author considers the quasilinear differential equations \begin{gather*} \left(r(t)\varphi(x')\right)'+ q(t)f(x)=0\,,\quad \quad t\geq a\\ \intertext{and} \left(r(t)\varphi(x')\right)' + F(t,x)=\pm g(t)\,,\quad\quad t\geq a\,. \end{gather*} By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.
AMSclassification. 34D05, 34C11
Keywords. Nonoscillatory behavior, asymptotic decaying nonnegative solutions, fixed point theorem