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### On growth and zeros of differences of some meromorphic functions

Annales Polonici Mathematici

### A free boundary problem arising in magnetohydrodynamic system

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### On zeros of differences of meromorphic functions

Annales Polonici Mathematici

Let f be a transcendental meromorphic function and $g\left(z\right)=f\left(z+c₁\right)+\cdots +f\left(z+{c}_{k}\right)-kf\left(z\right)$ and ${g}_{k}\left(z\right)=f\left(z+c₁\right)\cdots f\left(z+{c}_{k}\right)-{f}^{k}\left(z\right)$. A number of results are obtained concerning the exponents of convergence of the zeros of g(z), ${g}_{k}\left(z\right)$, g(z)/f(z), and ${g}_{k}\left(z\right)/{f}^{k}\left(z\right)$.

### Multiple end solutions to the Allen-Cahn equation in ${ℝ}^{2}$

Séminaire Laurent Schwartz — EDP et applications

An entire solution of the Allen-Cahn equation $\Delta u=f\left(u\right)$, where $f$ is an odd function and has exactly three zeros at $±1$ and $0$, e.g. $f\left(u\right)=u\left({u}^{2}-1\right)$, is called a $2k$ end solution if its nodal set is asymptotic to $2k$ half lines, and if along each of these half lines the function $u$ looks (up to a multiplication by $-1$) like the one dimensional, odd, heteroclinic solution $H$, of ${H}^{\text{'}\text{'}}=f\left(H\right)$. In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space of such solutions....

### On $f$-derivations of BCI-algebras.

International Journal of Mathematics and Mathematical Sciences

### Exponential attractors for a nonclassical diffusion equation.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Advancing analysis capabilities in ANSYS through solver technology.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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