We consider the boundedness solutions of a certain fourth-order nonlinear and nonhomogeneous differential equation. prove that this equation are bounded byCauchy formula

Keywords: Difference equations Boundary value problems Symmetric Green's function Fixed points Fourth-order Discrete Beam Lidstone Semipositone a b s t r a c t Various existence, multiplicity, and nonexistence results for nontrivial solutions to a non-linear discrete fourth-order Lidstone boundary value problem with dependence on two parameters are given, using a symmetric Green's function appr...

A class of nonlinear fourth-order telegraph-diffusion equations TDE for image restoration are proposed based on fourth-order TDE and bilateral filtering. The proposed model enjoys the benefits of both fourth-order TDE and bilateral filtering, which is not only edge preserving and robust to noise but also avoids the staircase effects. The existence, uniqueness, and stability of the solution for ...

In this paper, we construct some fourth-order modifications of Newton’s method for solving nonlinear equations. Any two existing fourth-order methods can be effectively used to give rise to new fourth-order methods. Per iteration the new methods require two evaluations of the function and one of its first-derivative. Numerical examples are given to show the performance of the presented methods....

In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.

To improve the accuracy of digital image edge detection, an ENO nonlinear fourth-order interpolation based subpixel edge detection algorithm was proposed in this paper. A stencil was constructed through classical Canny operator, followed by processing gray images to generate gradient images. ENO nonlinear fourth-order interpolation was applied in the gradient direction of target edges, and then...

The modified differential transform method (MDTM), Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obta...

In this article we propose a novel image denoising and restoration system based on a combination of second and fourth order partial differential equations. We consider a variational scheme that minimizes a energy functional composed of functions of gradient magnitude and of absolute value of Laplacian of image intensity. Then the corresponding Euler-Lagrange equation is computed, a PDE model ba...