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
$$m,n\......
Reduction formulas for higher order derivations and a hypergeometric identity
Aequationes mathematicae - Tập 95 - Trang 1053-1065 - 2021
A derivation (of order 1) satisfies the reduction formula
$$f(x^k) = kx^{k-1}f(x)$$
for any integer k. In this article we find corresponding reduction formulas for derivations of higher order on commutative rings. More precisely, for every derivation f of order n and every positive integer k we fi......
Nonuniform exponential dichotomies and Fredholm operators for flows
Aequationes mathematicae - Tập 91 - Trang 301-316 - 2017
For the flow determined by a nonautonomous linear differential equation, we characterize the existence of a strong nonuniform exponential dichotomy in terms of the Fredholm property of a certain linear operator. We consider both cases of one-sided and two-sided exponential dichotomies. Moreover, we use the characterizations to establish the robustness of the notion of a strong nonuniform exponenti......
Remarks on hyperstability of the Cauchy functional equation
Aequationes mathematicae - Tập 86 Số 3 - Trang 255-267 - 2013
A note on functional equations connected with the Cauchy mean value theorem
Aequationes mathematicae - - 2018
The aim of this paper is to describe the solution (f, g) of the equation
$$\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
......
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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