Global Analysis and Discrete Mathematics
Volume:1 Issue: 1, Summer and Autumn 2016

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

In this paper, we have proposed and analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations.

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has these properties. Finally a numerical example is solved to illustrate the scheme of analysis.

In this paper we consider the dynamics of the real polynomials of degree d 1 with a fixed point of multiplicity d ≥ 2. Such polynomials are conjugate to fa,d(x) = axd(x−1), a ∈ R\{0}, d ∈ N. Our aim is to study the dynamics fa,d in some special cases.

The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.