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# Article

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Keywords:
nonoscillatory behavior; asymptotic decaying nonnegative solutions; fixed point theorem
Summary:
The author considers the quasilinear differential equations \begin{gather} \left(r(t)\varphi (x^{\prime })\right)^{\prime }+ q(t)f(x)=0\,,\quad \quad t\ge a\\ \multicolumn{2}{l}{\text{and}}\\ \left(r(t)\varphi (x^{\prime })\right)^{\prime } + F(t,x)=\pm g(t)\,,\quad \quad t\ge a\,. \end{gather} By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.
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