Results 1 to 10 of about 71,517 (254)

Functional equations in real-analytic functions [PDF]

Studia Mathematica, 2000
Consider the functional equation \[ \phi(x)=g(x,\phi(Fx)) \] where \(F:X\to X\) (\(X\) real analytic manifold countable at infinity, \(dim X=m\)), \(g:X\times \mathbb R^n \to \mathbb R^n\) and \(\phi:X \to \mathbb R^n\) are real-analytic functions (\(\phi\) is the unknown function).
Belitskii, G., Tkachenko, V.
exaly   +3 more sources

Absence of Real Roots of Characteristic Functions of Functional Differential Equations with Nine Real Parameters

Taiwanese Journal of Mathematics, 2011
The authors consider the first order neutral functional-differential equation of the form \[ au'(t)+bu(t)+(cu'(t+\sigma)+du(t+\sigma))+xu(t+\delta)+yu(t+\tau)=0, \] where \(a, b, c, d, x, y, \sigma, \delta, \tau\) are real parameters, and intend to find the exact region containing these parameters such that all solutions of the above equation oscillate.
Shao-Yuan Huang
exaly   +3 more sources

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

SciPost Physics, 2022
In this paper, the real-time dynamics of the $O(4)$ scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path.
Yang-yang Tan, Yong-rui Chen, Wei-jie Fu
doaj   +1 more source

Abel’s Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions [PDF]

Integral Equations and Operator Theory, 2014
We obtain full description of eigenvalues and eigenvectors of composition operators Cϕ : A (R) → A (R) for a real analytic self map ϕ : R → R as well as an isomorphic description of corresponding eigenspaces. We completely characterize those ϕ for which Abel’s equation f ◦ ϕ = f + 1 has a real analytic solution on the real line.
Bonet, José, Domański, Paweł
openaire   +3 more sources

Features of Loss of Stability of the Work of Two-Link Mechanisms That Have an Infinite Number of Degrees of Freedom [PDF]

International Journal of Mathematical, Engineering and Management Sciences, 2018
Mechanisms consisting of two links, a leading (engine) and a slave (executive body), which are connected by long lines of force, are considered. With the use of the new method, general equations are derived in Laplace images describing the oscillations ...
Leonid Kondratenko, Lubov Mironova
doaj   +1 more source

On qualitative behavior of multiple solutions of quasilinear parabolic functional equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations for $t\in (0,\infty )$ with certain nonlocal terms.
László Simon
doaj   +1 more source

The real-analytic solutions of the Abel functional equation [PDF]

Studia Mathematica, 1999
The authors continue to investigate the Abel equation \[ \phi(Fx)-\phi(x)=1, \qquad x \in X \] where \(\phi:X \to \mathbb R\) is the unknown function, \(X\) is a topological space and \(F:X \to X\) is a continuous mapping. In a previous paper [Stud. Math. 127, No.
Belitskii, G., Lyubich, Yu.
openaire   +2 more sources

Spectral analysis of an operator associated with linear functional differential equations and its applications

Electronic Journal of Qualitative Theory of Differential Equations, 2000
The spectral set of an operator which is associated with linear autonomous functional differential equations is determined. The consequence is applied to study the admissibility of linear autonomous functional differential equations for the function ...
Satoru Murakami, Toshiki Naito, N. V. Minh   +2 more
doaj   +1 more source

Multiple solutions of nonlinear partial functional differential equations and systems

Electronic Journal of Qualitative Theory of Differential Equations, 2019
We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations.
László Simon
doaj   +1 more source

Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses on Time Scales

Advances in Difference Equations, 2009
By using a multiple fixed point theorem (Avery-Peterson fixed point theorem) for cones, some criteria are established for the existence of three positive periodic solutions for a class of higher-dimensional functional differential equations with impulses
Yongkun Li, Meng Hu
doaj   +2 more sources