Our purpose in this article is to study the asymptotic behavior of undamped evolution equations with fading memory on time-dependent spaces. By means theory processes spaces, a priori estimate and technique operator decomposition existence regularity attractors are, respectively, established critical case. At same time, we also obtain solution.

Transmit waveform design is one of the most important problems in active sensing and communication systems. This problem, due to the complexity and non-convexity, has been always the main topic of many papers for the decades. However, still an optimal solution which guarantees a global minimum for this multi-variable optimization problem is not found. In this paper, we propose an attracting met...

This paper develops a new implicit solution procedure for multibody systems based on three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward interpolation formula). The is second-order accurate, and the effective stiffness matrices of first two sub-steps are same. In this work, algorithmic parameters further optimized to minimize its local truncation error. Theoretical an...

This paper investigates the nonlinear observer design for mechanical systems, viz. nonlinear pendulum systems, undamped oscillators and Lienard systems. Explicitly, Sundarapandian’s Theorem (2002) for observer design for nonlinear systems is used to solve the problem of local exponential observer design for nonlinear pendulum systems, undamped oscillators and Lienard systems. Numerical examples...

We give conditions for the existence, uniqueness, and asymptotic stability of periodic solutions of a second-order differential equation with piecewise linear restoring and 2fl-periodic forcing where the range of the derivative of the restoring term possibly contains the square of an integer. With suitable restrictions on the restoring and forcing in the undamped case, we give a necessary and s...