scholarly journals A note on Kazdan–Warner equation on networks

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fabio Camilli ◽  
Claudio Marchi
Keyword(s):  
Differential Equation ◽  
Critical Case ◽  
Kirchhoff Type ◽  
Present Setting

Abstract We investigate the Kazdan–Warner equation on a network. In this case, the differential equation is defined on each edge, while appropriate transition conditions of Kirchhoff type are prescribed at the vertices. We show that the whole Kazdan–Warner theory, both for the noncritical and the critical case, extends to the present setting.

scholarly journals Asymptotic theory for a critical case for a general fourth-order differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 479-488
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Critical Case ◽  
Asymptotic Theory ◽  
Order Differential Equation ◽  
Fourth Order Equations ◽  
Fourth Order Differential Equation

In this paper we identify a relation between the coefficients that represents a critical case for general fourth-order equations. We obtained the forms of solutions under this critical case.

scholarly journals Half-linear Euler differential equations in the critical case

2011 ◽  
Vol 48 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Ondřej Došlý ◽  
Hana Haladová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Critical Case ◽  
Oscillatory Properties

Abstract We investigate oscillatory properties of the perturbed half-linear Euler differential equation . A perturbation is also allowed in the coefficient involving derivative.

A Galerkin–Newton Algorithm for Solution of a Kirchhoff-Type Static Equation

2021 ◽  
pp. 2150057
Author(s):  
Nikoloz Kachakhidze ◽  
Jemal Peradze ◽  
Zviad Tsiklauri
Keyword(s):  
Differential Equation ◽  
Discrete System ◽  
Total Error ◽  
Newton Iteration ◽  
System Of Equations ◽  
Static State ◽  
Kirchhoff Type ◽  
Static Equation ◽  
Newton Iteration Method ◽  
The Galerkin Method

In this paper, an algorithm is proposed to find an approximate solution for the Kirchhoff -type nonlinear differential equation, which describes the static state of a beam. The solution of the problem consists of two parts. First, we apply the Galerkin method. Next, to solve the obtained discrete system of equations, we use the Newton iteration method. The algorithm total error is estimated. The results of the numerical experiment are given.

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