New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

Download Full-text

Some Common Fixed Point Theorems for Generalized F-Contraction Involving w-Distance with Some Applications to Differential Equations

Mathematics ◽

10.3390/math7010032 ◽

2018 ◽

Vol 7 (1) ◽

pp. 32

Author(s):

Chirasak Mongkolkeha ◽

Dhananjay Gopal

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Differential Equations ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Order Differential Equation ◽

Existence Of Solutions ◽

Second Order Differential Equation ◽

Common Fixed Point Theorems

In this paper, we introduce the Ćirić type generalized F-contraction and establish certain common fixed point results for such F-contraction in metric spaces with the w-distances. In addition, we give some examples to support our results. Finally, we apply our results to show the existence of solutions of the second order differential equation.

Download Full-text

Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving w0-distance

Filomat ◽

10.2298/fil2012079i ◽

2020 ◽

Vol 34 (12) ◽

pp. 4079-4094

Author(s):

Iram Iqbal ◽

Muhammad Rizwan

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Fixed Point Theorems ◽

Order Differential Equation ◽

Electrical Energy ◽

Existence Of Solution ◽

Second Order ◽

Second Order Differential Equation ◽

Proper Generalization ◽

Generalized Distance

In the present paper, the aim is to obtain some new fixed point theorems for nonlinear F-contractions involving generalized distance to prove the existence of solution to second order differential equation related to conversion of solar energy to electrical energy. Non-trivial examples are also presented, to illustrate the obtained results and to show that new results are proper generalization of recently appeared results in the literature.

Download Full-text

A mechanical method for the solution of second-order linear differential equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100009804 ◽

1931 ◽

Vol 27 (4) ◽

pp. 546-552 ◽

Cited By ~ 1

Author(s):

E. C. Bullard ◽

P. B. Moon

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Boundary Conditions ◽

Order Differential Equation ◽

Second Order ◽

Linear Differential Equations ◽

Mechanical Method ◽

Order Linear ◽

Second Order Differential Equation ◽

Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

Download Full-text

Periodic solutions for periodic second-order differential equations with variable potentials

Journal of Applied Analysis ◽

10.1515/jaa-2018-0013 ◽

2018 ◽

Vol 24 (2) ◽

pp. 127-137

Author(s):

Jaume Llibre ◽

Ammar Makhlouf

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Periodic Solutions ◽

Order Differential Equation ◽

Sufficient Conditions ◽

Second Order ◽

Second Order Differential Equations ◽

Second Order Differential Equation ◽

Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Download Full-text

Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽

10.2478/s11534-009-0116-7 ◽

2010 ◽

Vol 8 (4) ◽

Cited By ~ 2

Author(s):

Octavio Cornejo-Pérez ◽

Haret Rosu

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Order Differential Equation ◽

Kdv Equation ◽

Travelling Wave ◽

Second Order ◽

Travelling Wave Solutions ◽

Second Order Differential Equation ◽

Wave Solutions ◽

Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

Download Full-text

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽

10.3390/sym11020143 ◽

2019 ◽

Vol 11 (2) ◽

pp. 143

Author(s):

Chayut Kongban ◽

Poom Kumam ◽

Juan Martínez-Moreno ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Random Fixed Point ◽

Contractive Mappings ◽

Random Differential Equations ◽

Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

Download Full-text

Weierstrass elliptic difference equations

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700013022 ◽

1987 ◽

Vol 35 (1) ◽

pp. 43-48 ◽

Cited By ~ 10

Author(s):

Renfrey B. Potts

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Difference Equations ◽

Elliptic Function ◽

Order Differential Equation ◽

Second Order ◽

Elliptic Difference ◽

First Order ◽

Second Order Differential Equation ◽

Weierstrass Elliptic Function

The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.

Download Full-text

Fixed point for F⊥-weak contraction

Mathematica Moravica ◽

10.5937/matmor2101113g ◽

2021 ◽

Vol 25 (1) ◽

pp. 113-122

Author(s):

Neeraj Garakoti ◽

Joshi Chandra ◽

Rohit Kumar

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Metric Space ◽

Order Differential Equation ◽

Second Order ◽

Weak Contraction ◽

Second Order Differential Equation

In this paper, we establish some fixed point results for F⊥-weak contraction in orthogonal metric space and we give an application for the solution of second order differential equation.

Download Full-text

Integrals of the Differential Equations ẍ + f ( s ) x = 0

Canadian Mathematical Bulletin ◽

10.4153/cmb-1967-017-2 ◽

1967 ◽

Vol 10 (2) ◽

pp. 191-196 ◽

Cited By ~ 1

Author(s):

R. Datko

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Stability Problem ◽

Additional Assumption ◽

Order Differential Equation ◽

Second Order ◽

Extensive Survey ◽

Second Order Differential Equation ◽

All Solutions ◽

New Criterion

In this note we consider a relatively ancient stability problem: the behaviour of solutions of the second order differential equation ẍ + f(s) x = 0, where f(s) tends to plus infinity as s tends to plus infinity. An extensive survey of the literature concerning this problem and a resume of results may be found in [ l ]. More recently McShane et a l. [2] have shown that the additional assumption f(s) ≥ 0 is not sufficient to guarantee that all solutions tend to zero as s tends to infinity. Our aim is to demonstrate a new criterion for which all solutions do have the above property. This criterion overlaps many of the cases heretofore considered.

Download Full-text

On the integrability of solutions of perturbed non-linear differential equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500025221 ◽

1977 ◽

Vol 77 (3-4) ◽

pp. 309-318 ◽

Cited By ~ 5

Author(s):

Paul W. Spikes

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Order Differential Equation ◽

Sufficient Conditions ◽

Second Order ◽

Linear Differential Equations ◽

Second Order Differential Equation ◽

All Solutions ◽

Non Linear ◽

Linear Differential

SynopsisSufficient conditions are given to insure that all solutions of a perturbed non-linear second-order differential equation have certain integrability properties. In addition, some continuability and boundedness results are given for solutions of this equation.

Download Full-text