A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable e...

In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form (a(t)([x(t)− p(t)x(h(t))])) + q(t)x(g(t)) = 0, t ∈ [t0,∞)T, where α and β are quotients of positive odd integers with β ≤ α. 2000 AMS Classification: 34C10, 34C15.

We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition A2u + CAU = bu+ + f in 0, where R is a bounded open set in Rn with smooth boundary and the nonlinearity bu+ crosses eigenvalues of A2 + CA. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearit...

The rule of trajectory structure for fourth-order nonlinear difference equation xn 1 x a n−2 xn−3 / x a n−2xn−3 1 , n 0, 1, 2, . . . , where a ∈ 0, 1 and the initial values x−3, x−2, x−1, x0 ∈ 0,∞ , is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4 , 3−, ...

We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature. This is an open access article distributed under the Creative Commons Attribution Li...

The governing equations for the unsteady flow of a uniformly conducting incompressible fourth-grade fluid due to noncoaxial rotations of a porous disk and the fluid at infinity are constructed. The steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied. The nonlinear ordinary differential equations resulting from the balance of momen...

With the help of a multi-scale expansion method, Lou derived a type of the higher-order nonlinear Schrödinger equation from the nondimensional barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a betaplane channel to describe nonlinear modulated Rossby waves [1]. This higher-order nonlinear Schrödinger equation includes fourth-order dispersion with ...

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forwar...

The structure of symplectic integrators up to fourth order can be completely and analytically understood when the factorization (split) coefficients are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and nonforw...