Fred Gross

Bio: Fred Gross is an academic researcher from University of Maryland, Baltimore. The author has contributed to research in topics: Functional equation & Prime (order theory). The author has an hindex of 3, co-authored 5 publications receiving 36 citations.

The phragmén-lindelöf principle and a class of functional differential equations

Abstract: Publisher Summary This chapter discusses the Phragmen-Lindelof principle and a class of functional differential equations. The experimental mathematics and the computerhave played a role in motivating the work on this principle. One added fruitful result of using the computer is that many graphs were produced.Since graphs of solutions to retarded ordinary differential equations are rather rare, one include some of the more interesting oscillatory ones. The work was motivated by the results of systematic computer studies made of particular cases. These experiments suggested the likelihood of unbounded oscillatory solutions to equation.

Entire solutions of Fermat type differential-difference equations

Abstract: We mainly discuss entire solutions with finite order of the following Fermat type differential-difference equations $$\begin{array}{ll}(f)^{n}+f(z+c)^{m}=1;\\f^{\prime}(z)^{n}+f(z+c)^{m}=1;\\ f^{\prime}(z)^{n}+[f(z+c)-f(z)]^{m}=1,\end{array}$$ where m, n are positive integers.

On Entire Solutions of Some Differential-Difference Equations

Abstract: In this paper, we will investigate the properties of entire solutions with finite order of the Fermat type difference or differential-difference equations. This is continuation of a recent paper (Liu et al. in Arch. Math. 99, 147–155, 2012). In addition, we also consider the value distribution and growth of the entire solutions of linear differential-difference equation \(f^{(k)}(z)=h(z)f(z+c),\) where \(h(z)\) is a non-zero meromorphic function, \(c\) is a non-zero constant. Our results partially answer the question given in Liu et al. (Arch. Math. 99, 147–155, 2012).