scholarly journals The classical Bertrand-Darboux problem

2008 ◽  
Vol 151 (4) ◽  
pp. 3230-3244 ◽  
Author(s):  
R. G. Smirnov
Keyword(s):  
Darboux Problem

Kneser's theorem for weak solutions of the Darboux problem in Banach spaces

1993 ◽  
Vol 20 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Staniśław Szufla
Keyword(s):  
Banach Spaces ◽  
Weak Solutions ◽  
Darboux Problem

The Darboux problem involving the distributional Henstock–Kurzweil integral

2012 ◽  
Vol 55 (1) ◽  
pp. 197-205 ◽  
Author(s):  
Yueping Lu ◽  
Guoju Ye ◽  
Ying Wang ◽  
Wei Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Schauder Fixed Point Theorem ◽  
Darboux Problem ◽  
Schauder Fixed Point ◽  
Schäuder Fixed Point Theorem

AbstractIn this paper, using the Schauder Fixed Point Theorem and the Vidossich Theorem, we study the existence of solutions and the structure of the set of solutions of the Darboux problem involving the distributional Henstock–Kurzweil integral. The two theorems presented in this paper are extensions of the previous results of Deblasi and Myjak and of Bugajewski and Szufla.

scholarly journals On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints

1996 ◽  
Vol 37 (3) ◽  
pp. 354-391 ◽  
Author(s):  
H. D. Tuan
Keyword(s):  
Constraint Qualification ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Regularity Assumption ◽  
Darboux Problem ◽  
Continuous Version ◽  
Open Mapping Theorem ◽  
Solution Sets ◽  
Relaxation Theorem ◽  
Endpoint Constraints

AbstractWe prove a continuous version of a relaxation theorem for the nonconvex Darboux problem xlt ε F(t, τ, x, xt, xτ). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

Second Darboux problem for the wave equation with a power-law nonlinearity

2013 ◽  
Vol 49 (12) ◽  
pp. 1577-1595 ◽  
Author(s):  
S. S. Kharibegashvili ◽  
O. M. Dzhokhadze
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Darboux Problem

scholarly journals THE DARBOUX AND KOSHI PROBLEM FOR LINEAR HYPERBOLIC EQUATIONS WITH CONSTANT COEFFICIENTS

2021 ◽  
Vol 6 (12(81)) ◽  
pp. 15-18
Author(s):  
Z. Usipbek ◽  
D. Aubakir ◽  
D. Bexapar ◽  
Zh. Ashirkhan ◽  
A. Shekerbek
Keyword(s):  
Hyperbolic Equations ◽  
Explicit Representation ◽  
Darboux Problem ◽  
Constant Coefficients ◽  
Linear Hyperbolic Equations

Many phenomena of mechanics, physics, and biology are reduced to the study of hyperbolic equations. In order to describe these phenomena completely, the Darboux problem is posed for hyperbolic equations, and for further studies, an explicit representation of the problem under consideration is necessary. In this article discusses, we study the Darboux and Koshi problems for linear hyperbolic equations with constant coefficients.

scholarly journals Ulam-Hyers stability of Darboux-Ionescu problem

2021 ◽  
Vol 37 (2) ◽  
pp. 211-216
Author(s):  
DANIELA MARIAN ◽  
SORINA ANAMARIA CIPLEA ◽  
NICOLAE LUNGU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Darboux Problem ◽  
Partial Differential ◽  
Doctoral Thesis ◽  
Rassias Stability

In his doctoral thesis, D. V. Ionescu has considered Darboux problem for partial differential equations of order two with modified argument. The Darboux-Ionescu problem was studied in some general cases by I. A. Rus. In this paper we study Ulam-Hyers stability and Ulam-Hyers-Rassias stability for this problem considered by I. A. Rus, using inequalities of Wendorff type.

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