Asymptotic behaviour of oscillatory solutions of the fourth-order nonlinear differential equation with quasiderivates y[4] + r(t)f(y) = 0 is studied.

The method of exact linearization nonlinear ordinary differential equations (ODE) of order n suggested by one of the authors is demonstrated in [1, 2]. This method is based on the factorization of nonlinear ODE through the first order nonlinear differential the operators, and is also based on using both point and nonpoint, local and nonlocal transformations. Exact linearization of autonomous th...

∆p := ∆(|∆u|p−2∆u) is the operator of fourth order, so-called the p-biharmonic (or p-bilaplacian) operator. For p = 2, the linear operator ∆2 = ∆2 = ∆ · ∆ is the iterated Laplacian that to a multiplicative positive constant appears often in the equations of Navier-Stokes as being a viscosity coefficient, and its reciprocal operator noted (∆2)−1 is the celebrated Green’s operator (see [8]). Exis...

We use the bivariate spline method to solve the steady state Navier-Stokes equations numerically. The bivariate spline we use in this paper is the space of splines of smoothness r and degree 3r over triangulated quadrangu-lations. The stream function formulation for the steady state Navier-Stokes equations is employed. Galerkin's method is applied to the resulting nonlinear fourth order equatio...

We use the bivariate spline nite elements to numerically solve the steady state NavierStokes equations. The bivariate spline nite element space we use in this paper is the space of splines of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the steady state Navier-Stokes equations is employed. Galerkin's method is applied to the resulting nonlin...