A Class of functional equations which have entire solutions

Entire Solutions to a Class of Fully Nonlinear Elliptic Equations

We study nonlinear elliptic equations of the form F (Du) = f(u) where the main assumption on F and f is that there exists a one dimensional solution which solves the equation in all the directions ξ ∈ Rn. We show that entire monotone solutions u are one dimensional if their 0 level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Distributional and Entire Solutions of Linear Functional Differential Equations

A unified approach to the study of generallzed-functlon and entire solutions to linear functional differential equations with polynomial coefficients is suggested.

Smooth Solutions of a Class of Iterative Functional Differential Equations

and Applied Analysis 3 where i, j, and k are nonnegative integers. Let I be a closed interval in R. By induction, we may prove that x∗jk t Pjk ( x10 t , . . . , x1,j−1 t ; . . . ;xk0 t , . . . , xk,j−1 t ) , 1.11 βjk Pjk ⎛ ⎜⎝ j terms { }} { x′ ξ , . . . , x′ ξ ; . . . ; j terms { }} { x k ξ , . . . , x k ξ ⎞ ⎟⎠, 1.12 Hjk Pjk ⎛ ⎜⎝ j terms { }} { 1, . . . , 1; j terms { }} { M2, . . . ,M2; . . . ...

Growth of solutions of a class of linear differential equations with entire coefficients

In this paper we will investigate the growth of solutions of the linear differential equation f (n) + Pn−1(z)e f (n−1) + · · · + P0(z)ef = 0 where P0, . . . , Pn−1 are polynomials.