Existence and Uniqueness of Homoclinic Solution for a Rayleigh Equation with a Singularity

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Shiping Lu ◽  
Xuewen Jia
Keyword(s):  
Existence And Uniqueness ◽  
Homoclinic Solution ◽  
Rayleigh Equation

scholarly journals Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lijuan Chen ◽  
Shiping Lu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Homoclinic Orbit ◽  
Limit Point ◽  
Existence And Uniqueness ◽  
Homoclinic Solution ◽  
Second Order ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem ◽  
Second Order Differential Equations

The authors study the existence and uniqueness of a set with2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of2kT-periodic solutions.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

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