Differential Equations Of Degree Research Articles

Presenting a Differential Equation Strengthened by the Cross Braces for Roof System

Plate girders structures is a major industry, much used in the systems covered by these beams, reduce deflection and decrease the maximum bending moment can be considered as a development methodology that way, by the cross beams or braced beams element perpendicular to the girders is provided. In this paper, the effect of stiffness and distance elements development (braced beams) are studied. Differential equation of degree four governing the behavior of the partial structures a quadratic relationship is determined by solving the following mathematical transformations and the fundamental equations are derived. The resulting equations are solved by a practical problem and the answer to the problem. The modeling results are compared with the SAP2000 program shows that highly accurate implementation and compliance. It is thus stiffness changing elements within the cross can be different amounts of stress, bending moment and improved cover and roof system and regulation forces to be calculated. In the proposed method by changing several parameters affecting. Calculate the amount of stress and reduced bending moments and an optional stress adjustment achieved. Other factors, including the backing, boundary conditions, a subsidiary of loading and shooting the junction depth of the main beam are effective in regulating stress.

Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four

Li and Llibre in [J. Differential Equations252 (2012) 3142–3162] proved that a Liénard system of degree four: dxdt=y−(ax+bx2+cx3+x4), dydt=−x has at most one limit cycle. Moreover, the limit cycle is stable and hyperbolic if it exists. Based on their works, the aim of this paper is to give the complete bifurcation diagram and global phase portraits in the Poincaré disc of this system further. First we analyze the equilibria at both finity and infinity. Then, a necessary and sufficient condition for existence of separatrix loop is founded by the rotation property. Moreover, a necessary and sufficient condition of the existence of limit cycles is also obtained. Finally, we show that the complete bifurcation diagram includes one Hopf bifurcation surface and one bifurcation surface of separatrix loop.

Solving Some Kinds of Third Order Partial Differential Equations of Degree Four with Three Independent Variables

In this paper, we find a solution for some kinds of nonlinear third order partial differential equations of homogeneous degree with three independent variables

Uniqueness of limit cycles for Liénard differential equations of degree four

We prove that any classical Liénard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C.C. Pugh (1977) [4] about the number of limit cycles for polynomial Liénard differential equations for n = 4 .

Topological classification of polynomial complex differential equations with all the critical points of centre type

In this paper, we study the global phase portrait of complex polynomial differential equations of degree n of the form , having all their critical points of centre type. We give the exact number of topologically different phase portraits on the Poincaré disk when and in the remaining cases, an upper bound for this number in terms of n.

Limit Cycles of a Class of Hilbert's Sixteenth Problem Presented by Fractional Differential Equations

The second part of Hilbert's sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert's sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equations.

Exact solution of the row-convex polygon perimeter generating function

An explicit expression is obtained for the perimeter generating function G(y)= Sigma n>or=2 any2n for row-convex polygons on the square lattice, where an is the number of 2n step row-convex polygons. An asymptotic expression for an approximately A mu nn-3/2 is obtained, where mu =3+22 and A are given. The authors also show that the generating function is an algebraic function and that it satisfies an inhomogeneous linear differential equation of degree three.