Geodesic
The trajectory controllability of second order semi-linear systems using a functional analytic approach
Journal of computational and engineering mathematics, Tome 11 (2024) no. 4, pp. 22-32.

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This article examines the trajectory controllability (TC) of second-order evolution systems while taking impulses into account. A cosine family of operators produced by the linear component of the system, the integral version of Gronwall's inequality, and the idea of nonlinear functional analysis were used to describe the TC findings. Applications for finite- and infinite-dimensional systems of trajectory-controlled systems are given.
Keywords: trajectory controllability, Gronwall's inequality, lipschitz nonlinearity, nonlinear systems. 
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     title = {The trajectory controllability of second order semi-linear systems using a functional analytic approach},
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V. Shah; J. Sharma; M. E. Samei; G. Trivedi. The trajectory controllability of second order semi-linear systems using a functional analytic approach. Journal of computational and engineering mathematics, Tome 11 (2024) no. 4, pp. 22-32. http://geodesic.mathdoc.fr/item/JCEM_2024_11_4_a2/