Asymptotic behavior of a laminated beam with nonlinear delay and nonlinear structural damping

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Nonlinear Vibration Analysis of a cantilever beam with nonlinear geometry

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don...

Nonlinear Beam Equation with Indefinite Damping

We consider the nonlinear beam equation utt + a(x)ut − f(ux)x + uxxxx = 0 in a bounded interval (0, 1) ⊂ R. The equation has an indefinite damping term, i.e., with a damping function a = a(x) possibly changing sign. For this non-dissipative situation we prove the exponential stability of the corresponding linearized system provided ā = ∫ 1 0 a(x)dx > 0 and ‖ a− ā ‖L2≤ τ , for τ small enough. We...

Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

and Applied Analysis 3 here g t ≤ t∗ ≤ t.Hence x l ( g t ) ≥ x n−1 t∗ n − l − 1 ! t − g t n−l−1 ≥ x n−1 t n − l − 1 ! t − g t n−l−1. 1.7 Combining 1.7 and 1.5 , we see that x′ ( g t ) ≥ g l−1 t 2l−1 l − 1 ! n − l − 1 ! n−1 t t − g t n−l−1 1.8 for all large t. Lemma 1.2. Suppose the linear third-order differential equation z′′′ p t z 0, t ∈ I 1.9 has an eventually positive increasing solution on...

asymptotic behavior of multivariate reward processes with nonlinear reward functions