Results 151 to 160 of about 7,755,587 (178)

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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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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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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Entire solutions of Fermat type differential-difference equations

Archiv der Mathematik, 2012
Equations of the form \[ f(z)^n+f(z+c)^m=1,\, f'(z)^n+f(z+c)^m=1 \] and \[ f(z)^n+(f(z+c)-f(z))^m=1 \] are called Fermat-type differential-difference equations, where \(m, n\) are positive integers. The authors prove that some transcendental entire solutions of finite order to these equations, if any, can be expressed by sine functions.
Liu, Kai, Cao, Tingbin, Cao, Hongzhe
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Entire and meromorphic solutions of fermat type partial differential equations

Analysis, 1999
The author studies complex analytic solutions of PDEs of the form \({\mathfrak E}_{n,m}u:= \sum^n_{i= 1}(u_{z_i})^m= 1\), where \(u: \mathbb{C}^n\to \mathbb{C}\) (or \(\widehat{\mathbb{C}}\)), \(z_i\in \mathbb{C}\), \(n,m\in\mathbb{N}\). He uses and refines results from the better known situation where the \(u_{z_i}\) are replaced by general analytic ...
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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, Chinmayee Padhy, S. Das   +2 more
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Arithmetic of cyclotomic fields and Fermat-type equations

1994
Let l be any odd prime, and ζ a primitive l-th root of unity. Let C_l be the l-Sylow subgroup of the ideal class group of Q(ζ). The Teichmüller character w : Z_l → Z^*_l is given by w(x) = x (mod l), where w(x) is a p-1-st root of unity, and x ∈ Z_l. Under the action of this character, C_l decomposes as a direct sum of C^((i))_l, where C^((i))_l is the
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On Fermat-Type Functional and Partial Differential Equations

2012
This paper concerns entire and meromorphic solutions to functional and nonlinear partial differential equations of the form a 1 f m +a 2 g n =a 3 with function coefficients a k , k=1,2,3, where f and g are unknown functions or partial derivatives of an unknown function.
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On Ternary Equations of Fermat Type and Relations with Elliptic Curves

1997
The main purpose of this chapter is to show how arithmetical properties of elliptic curves E defined over global fields K and corresponding Galois representations are often related to interesting diophantine questions, amongst which the most prominent is without doubt Fermat’s Last Theorem, which has now become Wiles’ theorem.
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Transcendental solutions of Fermat-type functional equations in $$ \mathbb {C}^n $$

Analysis and Mathematical Physics, 2023
Vâsudeva Rao Allu, Molla Ahamed
exaly