Results 141 to 150 of about 7,755,587 (178)

Meromorphic solutions of Fermat type partial differential equations

Journal of Mathematical Analysis and Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.

exaly   +3 more sources

On Entire Solutions of Two Fermat-Type Differential-Difference Equations

Bulletin of the Iranian Mathematical Society
The authors investigate the equation \[ \begin{multlined} [a_0f(z)+a_1f^{\prime\prime}(z)+a_2f(z+c)]^2+2\omega [a_0f(z)+a_1f^{\prime\prime}(z)+a_2f(z+c)]\cdot \\ [b_0f(z)+b_1f^{\prime\prime}(z)+b_2f(z+c)]+[b_0f(z)+b_1f^{\prime\prime}(z)+b_2f(z+c)]^2=e^{\alpha z+\beta}, \end{multlined} \] where \(\alpha, \beta, \omega^2(\neq 0,1), c(\neq 0), a_i, b_i (i=
Yihui Gong, Qi Yang
exaly   +3 more sources

ON THE TRANSCENDENTAL SOLUTION OF THE FERMAT TYPE Q-SHIFT EQUATION

Electronic Journal of Mathematical Analysis and Applications, 2023
Summary: In Nevanlinna's value distribution theory we considering some basic terms like \(T(r, f), N(r, f), m(r, f)\) etc., and let \(f^m(z) +q(z) [f^n \Delta^q_\eta f]^{(k)}=p(z)\) be a non-linear \(q\)-th order difference equation and \(f(z)\) be a transcendental meromorphic function with finite order \(m\), \(n\) and \(k\) be a positive integers ...
Naveenkumar, S. H., Chaithra, C. N., Jayarama, H. R.   +2 more
openaire   +1 more source

Generalized Fermat equations: A miscellany

International Journal of Number Theory, 2015
This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which ...
Michael Bennett, Imin Chen, Soroosh Yazdani   +2 more
exaly   +2 more sources

On Generalized Fermat Type Functional Equations

Computational Methods and Function Theory, 2006
The authors treat functional equations of the form \[ \sum^p_{j=1} a_j(z) f^{k_j}_j(z)\equiv 1,\tag{1} \] where \(p\geq 2\) an integer, and \(a_j(z)\), \(j= 1,\dots,p\) are meromorphic functions. They consider the solution \((f_1,\dots, f_p)\) of (1) satisfying a growth condition \(T(r, a_j)= o(\max_{1\leq k\leq p}T(r, f_k))\), \(1\leq j\leq p\), as ...
Lahiri, Indrajit, Yu, Kit-Wing
openaire   +2 more sources

Restrictions on meromorphic solutions of Fermat type equations

Proceedings of the Edinburgh Mathematical Society, 2020
AbstractThe Fermat type functional equations $(*)\, f_1^n+f_2^n+\cdots +f_k^n=1$, where n and k are positive integers, are considered in the complex plane. Our focus is on equations of the form (*) where it is not known whether there exist non-constant solutions in one or more of the following four classes of functions: meromorphic functions, rational ...
Gundersen, Gary G., Ishizaki, Katsuya, Kimura, Naofumi   +2 more
openaire   +2 more sources

NOTES ON FERMAT-TYPE DIFFERENCE EQUATIONS

Bulletin of the Australian Mathematical Society
AbstractWe consider the existence problem of meromorphic solutions of the Fermat-type difference equation $$ \begin{align*} f(z)^p+f(z+c)^q=h(z), \end{align*} $$ where $p,q$ are positive integers, and h has few zeros and poles in the sense that $N(r,h) + N(r,1/h) = S(r,h)$ . As a particular case, we consider $h=e^g$ , where g is an entire function.
ILPO LAINE, ZINELAABIDINE LATREUCH
openaire   +1 more source

An Identity of Fillipi Related to Fermat-Type Equations

2014
6 ...
Winkler, Mike, Fillipi, Andreas
openaire   +1 more source

On Meromorphic Solutions of the Fermat Type Difference Equations

Mediterranean Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qi, Xiaoguang, Yang, Lianzhong
openaire   +1 more source

Existence theorems for Fermat-type equations on Riemann surfaces

Complex Variables and Elliptic Equations
Shuang-shuang Yang, Liang-wen Liao
exaly   +2 more sources