[PDF] Top 20 Second order splitting for a class of fourth order equations

... which isn’t positive semi definite for any λ > 0. We will thus consider a situation where C does not induce a positive semi-definite bilinear form. Note that this work is not a direct generalisation of the results in ... See full document

... We note that for one high-order equation with degenerate nonlinear operator satisfy- ing a strengthened ellipticity condition, regularity of solutions was studied in [4, 5] (non- degenerate case) and in [6, 7] ... See full document

... difference equations. Compared to second-order difference equations, the study of higher-order equations, and in particular fourth-order equations (see, ...of ... See full document

... in order to prove the existence of the optimal control potentials for the optimal control problems deduced from the non-degenerate potential problems, we find that the (strong) continuous dependence of solutions ... See full document

... differential equations is now highly appreciated as a natural theoretical basis for the mathematical modeling of the natural phenomena of various ...differential equations, we hereby refer the interested ... See full document

... for several values of m. But, they do not give a closed formula for general case. we list this parameters for m = 2, 3, 4, 5 and 6 in Table 1. Neta [15] has developed another fourth-order method requiring ... See full document

... a class of Goursat’s problems for non- linear hyperbolic equations, systems of nonlinear hyper- bolic equations and fourth-order linear hyperbolic equa- ... See full document

... By means of the concept of co-solution of certain algebraic equations associated to the problem, an analytical solution of initial value problems for coupled systems of second order diff[r] ... See full document

... To date, the asymptotic behavior of the solutions to deterministic difference equations has been discussed in many papers. Among them there are many papers about the oscillation of the solutions to deterministic ... See full document

... difference equations can be useful in their ...difference equations and systems of difference equations can be found, ...difference equations, although it is not quite a common ...difference ... See full document

... differential equations are generated, where, methods for their solution is very ...differential equations of the fourth order, with specific ...a class of Self-adjoint differential ... See full document

... Invariants are usually used in establishing some properties of solutions to an equation. Frequently they are useful in establishing the boundedness of solutions to a difference equation or a system of difference ... See full document

... difference equations arise from the study of molecular orbits, mathematical physics problems and the numerical difference approximation problems ...difference equations has attracted more and more ... See full document

... have also been employed to prove the existence of multiple periodic solutions of mixed type differential equations in []. When (.) reduces to the special case, see system (.), we obtain a more accurate result ... See full document

... We have two aims in this paper. The first aim is to remove the condition (1.5) in Theorem 1.1 and to demonstrate this with an example. The second goal is to extend the technique developed by Rogovchenko and Tuncay ... See full document

... On the Oscillation of Solutions of a Class of Linear Fourth Order Differential Equations, Pacific J.. An Ordering of Oscillation Types for Anal.[r] ... See full document

... by presenting simple criteria for the oscillation of all solutions of (1.1). Most importantly, we stress that the nonexistence of eight possible classes of nonoscillatory solutions (see Lemma 1) is shown only through two ... See full document

... nonlinear equations for simple roots by using inverse function ...a class of optimal fourth-order methods by using one function and two first derivative evaluations per full cycle is given ... See full document

... In this article, a class of fourth-order difference equations with quasi-differences and deviating argument is considered. We state a new oscillation theorem for the sublinear case and we ... See full document

... We consider the dynamical properties for a kind of fourth-order rational difference equations. The key is for us to find that the successive lengths of positive and negative semicycles for non- ... See full document