Normal form theory is a technique for transforming the ordinary differential equations describing nonlinear dynamical systems into certain standard forms. Using a particular class of coordinate transformations, one can remove the inessential part of higher-order nonlinearities. Unlike the closely-related method of averaging, the standard development of normal form theory involves several techni...

This paper presents a comparative study of four control strategies for a flexible joint space manipulator. The considered control strategies consist in the classical Slotine and Li algorithm, a simple proportional derivative controller, a singular perturbation-based controller and a nonlinear backstepping controller. All control methodologies are assessed in numerical simulations for endpoint p...

In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian order $s\in (1/2,1)$ , singular nonlinearity and gradient term under various situations, including nonlocal contra-part classical Lienard vector equations, as well other versions know only in context second-order ODE. Our proofs are based on degree theory Perron's method, ...

A [Formula: see text]-Laplacian elliptic problem in the presence of both strongly singular and text]-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques sub-supersolution method to establish existence an unbounded branch positive solutions, which bounded text]-direction bifurcates from infinity at text]. As consequence result, we determine intervals ...