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.

scholarly journals The Existence of n Periodic Solutions on One Element n-Degree Polynomial Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-Xin
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Degree Polynomial ◽  
Polynomial Differential Equations ◽  
Polynomial Differential Equation

This paper deals with a class of one element n-degree polynomial differential equations. By the fixed point theory, we obtain n periodic solutions of the equation. This paper generalizes some related conclusions of some papers.

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 Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

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 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 Fixed point theory for multivalued generalized nonexpansive mappings

2012 ◽  
Vol 6 (2) ◽  
pp. 265-286 ◽  
Author(s):  
Jesús García-Falset ◽  
Enrique Llorens-Fuster ◽  
Elena Moreno-Gálvez
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Recent Literature ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
The Other

A very general class of multivalued generalized nonexpansive mappings is defined. We also give some fixed point results for these mappings, and finally we compare and separate this class from the other multivalued generalized nonexpansive mappings introduced in the recent literature.

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.

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