scholarly journals Unbounded Solutions for Functional Problems on the Half-Line

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Hugo Carrasco ◽  
Feliz Minhós
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Order Differential Equation ◽  
Upper And Lower Solutions ◽  
Half Line ◽  
Unbounded Solutions ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Fowler Equation ◽  
Functional Problems

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green’s functions, and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

scholarly journals Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 330
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Equations ◽  
General Class ◽  
Fixed Point Index ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

scholarly journals Solution of Fractional Differential Equations Utilizing Symmetric Contraction

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Aftab Hussain
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Continuous Mappings ◽  
Fractional Differential ◽  
Fixed Point Technique

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.

scholarly journals Fixed point for F⊥-weak contraction

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.

scholarly journals Periodic solutions of superlinear and sublinear state-dependent discontinuous differential equations

2021 ◽  
pp. 79-96
Author(s):  
Juan J. Nieto ◽  
José M. Uzal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Order Differential Equation ◽  
Point Of View ◽  
Discontinuous Differential Equations ◽  
Planar System ◽  
State Dependent ◽  
Existence Of Periodic Solutions

A classical, second-order differential equation is considered with state-dependent impulses at both the position and its derivative. This means that the instants of impulsive effects depend on the solutions and they are not fixed beforehand, making the study of this problem more difficult and interesting from the real applications point of view. The existence of periodic solutions follows from a transformation of the problem into a planar system followed by a study of the Poincaré map and the use of some fixed point theorems in the plane. Some examples are presented to illustrate the main results.

scholarly journals On the lower and upper solution method for higher order functional boundary value problems

2011 ◽  
Vol 5 (1) ◽  
pp. 133-146 ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Feliz Minhós ◽  
João Fialho
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Solution Method ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Boundary Functions ◽  
Lower And Upper Solution ◽  
Functional Boundary

The authors consider the nth-order differential equation ?(?(u(n?1)(x)))?= f(x, u(x), ..., u(n?1)(x)), for 2?(0, 1), where ?: R? R is an increasing homeomorphism such that ?(0) = 0, n?2, I:= [0,1], and f : I ?Rn ? R is a L1-Carath?odory function, together with the boundary conditions gi(u, u?, ..., u(n?2), u(i)(1)) = 0, i = 0, ..., n? 3, gn?2 (u, u?, ..., u(n?2), u(n?2)(0), u(n?1)(0)) = 0, gn?1 (u, u?, ..., u(n?2), u(n?2)(1), u(n?1)(1)) = 0, where gi : (C(I))n?1?R ? R, i = 0, ..., n?3, and gn?2, gn?1 : (C(I))n?1?R2 ? R are continuous functions satisfying certain monotonicity assumptions. The main result establishes sufficient conditions for the existence of solutions and some location sets for the solution and its derivatives up to order (n?1). Moreover, it is shown how the monotone properties of the nonlinearity and the boundary functions depend on n and upon the relation between lower and upper solutions and their derivatives.

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

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 324 ◽  
Author(s):  
Sujitra Sanhan ◽  
Winate Sanhan ◽  
Chirasak Mongkolkeha
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Generalized Pseudodistance

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.

scholarly journals EXISTENCE OF A SOLUTION FOR A SINGULAR DIFFERENTIAL EQUATION WITH NONLINEAR FUNCTIONAL BOUNDARY CONDITIONS

2007 ◽  
Vol 49 (2) ◽  
pp. 213-224 ◽  
Author(s):  
ALBERTO CABADA ◽  
JOSÉ ÁNGEL CID
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Diffusion Processes ◽  
Singular Differential Equation ◽  
Existence Of A Solution ◽  
Nonlinear Functional ◽  
Local Boundary ◽  
Functional Boundary ◽  
Non Local ◽  
Functional Boundary Conditions

AbstractIn this paper we deal with some boundary value problems related with diffusion processes in the presence of lower and upper solutions. Singularities as well as non local boundary conditions are allowed. We also prove the existence of extremal solutions and the uniqueness of solution for a particular case.

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