scholarly journals The Fixed Point Theory and the Existence of the Periodic Solution on a Nonlinear Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Ni Hua
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Differential Equation ◽  
Fixed Point Theory ◽  
Point Theory

This paper deals with a nonlinear differential equation, by using the fixed point theory. The existence of the periodic solution of the nonlinear differential equation is obtained; these results are new.

scholarly journals An Application of Fixed Point Theory to a Nonlinear Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Kaewcharoen ◽  
S. Plubtieng
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Nonlinear Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
New Family ◽  
Contractive Type

We introduce a new family of mappings on[0,+∞)by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems forα-ψ-contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.

scholarly journals A Criterion for the Existence of the Unique Periodic Solution of One-Dimensional Periodic Differential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ni Hua
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Lyapunov Method ◽  
Fixed Point Theory ◽  
Point Theory ◽  
One Dimensional ◽  
Periodic Differential Equation

In this paper, we discuss one-dimensional differential equation with ω -period. By using the fixed point theory, the existence of a periodic solution is obtained; by using the second Lyapunov method, the uniqueness and stability of the periodic solution are obtained.

Merton's Partial Differential Equation and Fixed Point Theory

1998 ◽  
Vol 105 (5) ◽  
pp. 412-420
Author(s):  
Franklin Lowenthal ◽  
Arnold Langsen ◽  
Clark T. Benson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Differential

The approximate solution of nonlinear Fredholm implicit integro-differential equation in the complex plane

2021 ◽  
Author(s):  
Samir Lemita ◽  
Sami Touati ◽  
Kheireddine Derbal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Approximate Solution ◽  
Integral Operator ◽  
Complex Plane ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Numerical Process

This paper’s purpose is to study the nonlinear Fredholm implicit integro-differential equation in the complex plane, where the term implicit integro-differential means that the derivative of unknown function is founded inside of the integral operator. Initially, according to Banach fixed point theory, we ensure that the equation has a unique solution under particular conditions. However, we exhibit a numerical process based on the conjunction between Nyström and Picard methods, for the sake of approximating solutions of this equation. In addition to that, the convergence analysis of this numerical process is demonstrated, and some illustrated numerical examples are presented.

scholarly journals Transformation Method for Generating Periodic Solutions of Abel’s Differential Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Ni Hua
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theory ◽  
Transformation Method ◽  
Point Theory ◽  
The Other ◽  
Alternative Method ◽  
Particular Solution

This paper deals with Abel’s differential equation. We suppose that r=r(t) is a periodic particular solution of Abel’s differential equation and, then, by means of the transformation method and the fixed point theory, present an alternative method of generating the other periodic solutions of Abel’s differential equation.

Nonlocal Differential Equations with Convolution Coefficients and Applications to Fractional Calculus

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christopher S. Goodrich
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Integral ◽  
Fixed Point Theory ◽  
Conjugate Problem ◽  
Point Theory ◽  
Liouville Type ◽  
Model Case ◽  
Fractional Differential

Abstract The existence of at least one positive solution to a large class of both integer- and fractional-order nonlocal differential equations, of which one model case is - A ⁢ ( ( b * u q ) ⁢ ( 1 ) ) ⁢ u ′′ ⁢ ( t ) = λ ⁢ f ⁢ ( t , u ⁢ ( t ) ) , t ∈ ( 0 , 1 ) , q ≥ 1 , -A((b*u^{q})(1))u^{\prime\prime}(t)=\lambda f(t,u(t)),\quad t\in(0,1),\,q\geq 1, is considered. Due to the coefficient A ⁢ ( ( b * u q ) ⁢ ( 1 ) ) {A((b*u^{q})(1))} appearing in the differential equation, the equation has a coefficient containing a convolution term. By choosing the kernel b in various ways, specific nonlocal coefficients can be recovered such as nonlocal coefficients equivalent to a fractional integral of Riemann–Liouville type. The results rely on the use of a nonstandard order cone together with topological fixed point theory. Applications to fractional differential equations are given, including a problem related to the ( n - 1 , 1 ) {(n-1,1)} -conjugate problem.

scholarly journals Existence Theory for Pseudo-Symmetric Solution to -Laplacian Differential Equations Involving Derivative

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
You-Hui Su ◽  
Weili Wu ◽  
Xingjie Yan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Symmetric Solution ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Existence Theory ◽  
Point Boundary

We all-sidedly consider a three-point boundary value problem for -Laplacian differential equation with nonlinear term involving derivative. Some new sufficient conditions are obtained for the existence of at least one, triple, or arbitrary odd positive pseudosymmetric solutions by using pseudosymmetric technique and fixed-point theory in cone. As an application, two examples are given to illustrate the main results.

Periodic Solutions for Nonlinear Differential Equation with Functional Delay

2008 ◽  
Vol 15 (4) ◽  
pp. 635-642
Author(s):  
Hafsia Deham ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Functional Delay

Abstract We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ([Proc. Amer. Math. Soc. 124: 2383–2390, 1996]) to show that the scalar nonlinear differential equation with functional delay 𝑥′(𝑡) = –𝑎(𝑡)𝑥3(𝑡) + 𝐺(𝑡, 𝑥3(𝑡 – 𝑟(𝑡))) has a periodic solution. It is not required that 𝑟(𝑡) be differentiable, while 𝑎 and 𝐺 are continuous with respect to their arguments.

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