Results 151 to 160 of about 81,722 (194)

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
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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
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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
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On Meromorphic Solutions of the Fermat Type Difference Equations

Mediterranean Journal of Mathematics
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Qi, Xiaoguang, Yang, Lianzhong
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Solutions and existence results for difference equations of fermat type

Rendiconti del Circolo Matematico di Palermo Series 2
The authors study the existence and explicit forms of solutions for the following two complex difference equations of Fermat-type: \[f(z)^{2}+\alpha(z)^{2}(e^{P(z)})^{2}f(z+c)^{2} =Q(z)e^{2\beta (z)},\] and \[f(z)^{2}+\alpha(z)^{2}(e^{P(z)})^{2}(\Delta _{c}f(z))^{2} =Q(z)e^{2\beta (z)},\] where \(\alpha(z), \beta (z), P(z)\), and \(Q(z)\) are non-zero ...
Sarkar, Nabadwip, Das, Pradip
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On Meromorphic Solutions of Some Fermat-Type Functional Equations

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
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Lu, J. T., Xu, J. F.
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Meromorphic Solutions for the Fermat-Type Differential-Difference Equations

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
By using Nevanlinna theory and its difference analogues, the authors study the entire solutions with hyper-order less than one to the following differential-difference equation \[ f(z)^{n}+(f'(z+c))^{m}=p(z)e^{r(z)}+q(z)e^{s(z)}. \] They classify the above equation into three cases: \begin{align*} f(z)^{n}+(f'(z+c))^{m}&=P_{1}(z)e^{A_{1}z^{k}}+Q_{1}(z ...
Zhu, X., Qi, X.
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Certain operator solutions to Fermat's type equation on Bergman spaces

Mathematical Foundations of Computing
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Pabitra Kumar Jena
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Meromorphic solutions of Fermat type partial differential equations

Journal of Mathematical Analysis and Applications, 2019
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Feng Lu
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ON ENTIRE SOLUTIONS OF FERMAT TYPE PARTIAL DIFFERENTIAL EQUATIONS

International Journal of Mathematics, 2004
We shall consider Fermat type partial differential equations in Cn, and give description and classification for entire solutions of the equations.
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