Investigation of a nonlinear singular equation with Hilbert kernel

1970 ◽  
pp. 197-205
Author(s):  
H. Š. Muhtarov
Keyword(s):  
Singular Equation ◽  
Hilbert Kernel

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

On the singular equation ?(u)t=?u

1995 ◽  
Vol 132 (3) ◽  
pp. 247-309 ◽  
Author(s):  
E. DiBenedetto ◽  
V. Vespri
Keyword(s):  
Singular Equation

Contact problem for wavy surfaces in the presence of an incompressible liquid and a gas in interface gaps

2018 ◽  
Vol 24 (11) ◽  
pp. 3381-3393 ◽  
Author(s):  
Oleh Kozachok ◽  
Rostyslav Martynyak
Keyword(s):  
Surface Tension ◽  
Contact Problem ◽  
Incompressible Liquid ◽  
Constant Pressure ◽  
Cauchy Kernel ◽  
Hilbert Kernel ◽  
Elastic Bodies ◽  
Laplace Formula ◽  
Interface Gaps ◽  
Wavy Surfaces

This paper presents a study on smooth elastic contact between two semi-infinite elastic bodies, one of which has a wavy surface, for the case when there are an incompressible liquid, not wetting the surfaces of the bodies, at the central region of each interface gap and a gas under constant pressure at the edges of each gap. Due to the surface tension of the liquid, a pressure drop occurs in the liquid and the gas, which is described by the Laplace formula. The formulated contact problem is reduced to a singular integral equation (SIE) with the Hilbert kernel, which is transformed into a SIE with the Cauchy kernel for a derivative of a height of the gaps. A system of transcendental equations for a width of each gap and a width of the gap region filled with the liquid is obtained from the condition of boundedness of the contact stresses at the gap ends and the condition of liquid amount conservation. It is solved numerically, and the dependences of the width and shape of the gaps, the width of the gap regions filled with the liquid and the contact approach of the bodies on the applied load and the surface tension of the liquid are analyzed.

Autocorrelation specification in singular equation systems

1994 ◽  
Vol 46 (4) ◽  
pp. 303-309 ◽  
Author(s):  
Giancarlo Moschini ◽  
Daniele Moro
Keyword(s):  
Singular Equation
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