A State-Dependent Dynamic Nonlinear Problems on Time Scales

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Considering the phenomena that depend on their past state or past history, it was noted that they were given more importance. The mathematical models of these phenomena can be explained by state-dependent differential equations or a self-referred type. This article is dedicated to studying the solvability of state-dependent or self-referred dynamic nonlinear problems on time scales. Here, we got the existence of at least one solution to state-dependent dynamic nonlinear problems on time scales and a unique solution it has. Further more, we obtained results on the dependency of solutions for state-dependent dynamic nonlinear problems on time scales with respect to initial values.

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