HIGHER-ORDER ESTIMATES FOR FULLY NONLINEAR DIFFERENCE EQUATIONS. II

Existence of Periodic Solutions for Higher-order Nonlinear Difference Equations

In this article, we study a higher-order nonlinear difference equation. By using critical point theory, we establish sufficient conditions for the existence of periodic solutions.

General Permanence Conditions for Nonlinear Difference Equations of Higher Order

w . m w . w . where f : 0, ` a 0, ` and the initial values x , . . . , x g 0, ` . 0 1ym Ž . In studying the global behavior of the solutions of Eq. 1 , we often need Ž . to establish that 1 is permanent, i.e., it has the property that every one of its solutions is eventually confined within a fixed compact interval regardless of the initial values chosen. Permanence is needed directly or indire...

Forced oscillation of higher order nonlinear difference equations

This paper considers the oscillation problem for forced nonlinear difference equations of the form 0096-3 doi:10 * Co E-m Dxn þ qnf ðxn sÞ 1⁄4 en: We study three cases: qn P 0, qn < 0 and qn is oscillatory. No restriction assumed in known literatures is imposed on the forcing term en. 2006 Elsevier Inc. All rights reserved.

Maximum Norm Error Estimates for Difference Schemes for Fully Nonlinear Parabolic Equations

This article establishes error bounds for finite difference schemes for fully nonlinear parabolic Partial Differential Equations (PDEs). For classical solutions the global error is bounded by a known constant times the truncation error of the exact solution. As a corollary, this gives a convergence rate of 1 or 2 for first or second order accurate schemes, respectively. Our results also apply f...

Higher Order Derivative Estimates for Finite-difference Schemes for Linear Elliptic and Parabolic Equations