Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations
Luisa Malaguti, Valentina Taddei (2005)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The paper deals with the quasi-linear ordinary differential equation with . We treat the case when is not necessarily monotone in its second argument and assume usual conditions on and . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano,...