Integral-Functional Equation Arising in the Study of an Inverse Problem for a Quasilinear Hyperbolic Equation

2018 ◽  
Vol 54 (9) ◽  
pp. 1180-1190 ◽  
Author(s):  
A. M. Denisov
Keyword(s):  
Functional Equation ◽  
Inverse Problem ◽  
Hyperbolic Equation ◽  
Integral Functional ◽  
Quasilinear Hyperbolic Equation

scholarly journals On a Certain Generalized Functional Equation for Set-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2243
Author(s):  
Yaroslav Bazaykin ◽  
Dušan Bednařík ◽  
Veronika Borůvková ◽  
Tomáš Zuščák
Keyword(s):  
Functional Equation ◽  
Integral Functional ◽  
Asplund Space ◽  
Invariant Metric ◽  
Real Vector ◽  
Linear Metric Space ◽  
Real Linear ◽  
The Right ◽  
Locally Convex ◽  
Generalized Type

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function F:X→cc(Y), where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X. Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where X=R2 and Y=Rn, n∈N, and G is the unitary group U(1).

scholarly journals On a global classical solution of a quasilinear hyperbolic equation

1989 ◽  
Vol 12 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Y. Ebihara ◽  
D. C. Pereira
Keyword(s):  
Hyperbolic Equation ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Torsional Vibrations ◽  
Global Classical Solution ◽  
Quasilinear Hyperbolic Equation ◽  
Global Classical Solutions

In this paper we establish the existence and uniqueness of global classical solutions for the equation which arises in the study of the extensional vibrations of thin rod, or torsional vibrations of thin rod.

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