Abstract
In this paper, the method of the quasilinearization technique in causal differential equations is applied to obtain upper and lower sequences with initial time difference in terms of the solutions of the linear causal differential equations that start at different initial times. It is also shown that these sequences converge to the unique solution of the nonlinear equation in causal differential equations uniformly and superlinearly.
Highlights
The most important applications of the quasilinearization method in causal di¤erential equations [5] has been to obtain a sequence of lower and upper bounds which are the solutions of linear causal di¤erential equations that converge superlinearly
The investigations of initial value problems of causal di¤erential equations where the initial time changes with each solution
The generalized quasilinearization technique in causal di¤erential equations is used to obtain upper and lower sequences in terms of the solutions of linear causal di¤erential equations that start at di¤erent initial times and bound the solutions of a given nonlinear causal di¤erential equation [5]
Summary
The most important applications of the quasilinearization method in causal di¤erential equations [5] has been to obtain a sequence of lower and upper bounds which are the solutions of linear causal di¤erential equations that converge superlinearly. The investigations of initial value problems of causal di¤erential equations where the initial time changes with each solution. The generalized quasilinearization technique in causal di¤erential equations is used to obtain upper and lower sequences in terms of the solutions of linear causal di¤erential equations that start at di¤erent initial times and bound the solutions of a given nonlinear causal di¤erential equation [5]. It is shown that these sequences converge to the unique solution of the nonlinear equation uniformly and superlinearly
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