Uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations. (English) Zbl 1423.34100
Summary: This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptions without sign conditions on the nonlinear part of the equation. Moreover, we prove a necessary condition for the existence of an asymptotically zero solution to the problem under consideration.
MSC:
| 34N05 | Dynamic equations on time scales or measure chains |
| 34K11 | Oscillation theory of functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
nonlinear dynamic equation; neutral-type equation; nonoscillation; Darbo fixed point theoremReferences:
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