Solutions to Riccati-s Problem as Functions of Initial Values

Isothermic and S-Willmore Surfaces as Solutions to Blaschke’s Problem

Note that Blaschke and his school only considered surfaces in 3-space and ignored the higher co-dimension case. In Sn this problem is still meaningful. It is known that the construction of Darboux pair of isothermic surfaces as well as dual Willmore surfaces has a generalization to Sn (see [4, 9] and [7]), and they still constitute solutions to the generalized Blaschke’s problem. Here we will s...

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition

In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

Improving the Accuracy of the Solutions of Riccati Equations

Approximate Solutions to the Binary Black Hole Initial Value Problem

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Ei...