*Correspondence: [email protected] 1College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China Full list of author information is available at the end of the article Abstract In this paper, by using the method of quasilinearization to discuss the periodic boundary value problem for a nonlinear singular differential system with ‘maxima’, we obtain monotone iterat...

We develop new quadrature rules for Isogeometric Analysis based on the solution of a local nonlinear problem. A simple and robust algorithm is developed to determine the rules which are exact for important B-Spline spaces of uniform and geometrically stretched knot spacings. We consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boun...

We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 ar...

By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation ΔΔpnΔxn − 1 δ − qnxn δ fn, xn has at least one homoclinic solution, where n ∈ Z, xn ∈ R, and f : Z × R → R is non periodic in n. Our conditions on the nonlinear term fn, xn are rather relaxed, and we generalize some existing results in the literature.

This paper presents the effect of preload on nonlinear dynamic behavior of a rigid rotor supported by two-lobe aerodynamic noncircular journal bearing. A finite element method is employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using Runge-Kutta method. To analyze the behavior of the rotor center in the horizontal and vertical directi...

Periodic steady-state (PSS) analysis of nonlinear oscillators has always been a challenging task in circuit simulation. We present a new way that uses numerical linear algebra to identify the PSS(s) of nonlinear circuits. The method works for both autonomous and excited systems. Using the harmonic balancing method, the solution of a nonlinear circuit can be represented by a system of multivaria...

We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in twoand three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schrödinger equation, sharing with these the propriety of being unstable against small norm (number...

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation is further investigated. By using the solutions of this equation, and a new general ansatz, we give some types of solutions of a class of nonlinear partial differential equations and MKdV equation. These solutions includes solitary wave solutions, singulary solitary solitary solutions...

The solution of the Langevin equation describing the dynamics of a Brownian particle in a tilted periodic potential in the overdamped limit is obtained in terms of a matrix continued fraction, allowing us to evaluate statistical averages governing the nonlinear response to a strong ac force. Pronounced nonlinear effects are observed for large values of the ac force. For a weak ac force and low ...

there has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. the popular poincare-bendixon theorem applies well to the former but not the latter (see [2] and [3]). we give a necessary condition for the existence of periodic solutions for the third order autonomous systems, t...