Aequationes mathematicae
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On Fermat Diophantine functional equations, little Picard theorem and beyond
Aequationes mathematicae - Tập 93 - Trang 425-432 - 2018
We discuss equivalence conditions for the non-existence of non-trivial
meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$
with integers $$m,n\ge 2$$ , from which other approaches to proving the little
Picard theorem are discussed....
Reduction formulas for higher order derivations and a hypergeometric identity
Aequationes mathematicae - Tập 95 - Trang 1053-1065 - 2021
A derivation (of order 1) satisfies the reduction formula $$f(x^k) =
kx^{k-1}f(x)$$ for any integer k. In this article we find corresponding
reduction formulas for derivations of higher order on commutative rings. More
precisely, for every derivation f of order n and every positive integer k we
find an explicit formula for $$f(x^k)$$ as a linear combination of
$$x^{k-1}f(x),x^{k-2}f(x^2), \ldots ,...
Nonuniform exponential dichotomies and Fredholm operators for flows
Aequationes mathematicae - Tập 91 - Trang 301-316 - 2017
For the flow determined by a nonautonomous linear differential equation, we
characterize the existence of a strong nonuniform exponential dichotomy in terms
of the Fredholm property of a certain linear operator. We consider both cases of
one-sided and two-sided exponential dichotomies. Moreover, we use the
characterizations to establish the robustness of the notion of a strong
nonuniform exponenti...
Remarks on hyperstability of the Cauchy functional equation
Aequationes mathematicae - Tập 86 Số 3 - Trang 255-267 - 2013
A note on functional equations connected with the Cauchy mean value theorem
Aequationes mathematicae - - 2018
The aim of this paper is to describe the solution (f, g) of the equation
$$\begin{aligned}{}[f(x)-f(y)]g'(\alpha x+(1-\alpha )y)= [g(x)-g(y)]f'(\alpha
x+(1-\alpha )y),\ x,y\in I, \end{aligned}$$ where $$I\subset \mathbb {R}$$ is an
open interval, $$f,g:I\rightarrow \mathbb {R}$$ are differentiable, $$\alpha $$
is a fixed number from (0, 1)....
Homological methods in the solution of certain functional equations
Aequationes mathematicae - Tập 31 - Trang 310-314 - 1986
A solution of the ‘converse canonical problem’ for multiple integrals in the calculus of variations
Aequationes mathematicae - Tập 6 - Trang 288-305 - 2005
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