scholarly journals Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
R. K. Pandey ◽  
A. K. Barnwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Dependent Data ◽  
Point Boundary ◽  
Nonnegative Solutions ◽  
Data Function

We study the existence of multiple nonnegative solutions for the doubly singular three-point boundary value problem with derivative dependent data function-(p(t)y′(t))′=q(t)f(t,y(t),p(t)y′(t)),0<t<1,y(0)=0,y(1)=α1y(η). Here,p∈C[0,1]∩C1(0,1]withp(t)>0on(0,1]andq(t)is allowed to be discontinuous att=0. The fixed point theory in a cone is applied to achieve new and more general results for existence of multiple nonnegative solutions of the problem. The results are illustrated through examples.

scholarly journals Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 526
Author(s):  
Ehsan Pourhadi ◽  
Reza Saadati ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

scholarly journals On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Said Melliani ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Uniqueness Results

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

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.

scholarly journals Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muthaiah Subramanian ◽  
Jehad Alzabut ◽  
Dumitru Baleanu ◽  
Mohammad Esmael Samei ◽  
Akbar Zada
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Boundary ◽  
Differential Systems ◽  
Fractional Differential

AbstractIn this paper, we examine the consequences of existence, uniqueness and stability of a multi-point boundary value problem defined by a system of coupled fractional differential equations involving Hadamard derivatives. To prove the existence and uniqueness, we use the techniques of fixed point theory. Stability of Hyers-Ulam type is also discussed. Furthermore, we investigate variations of the problem in the context of different boundary conditions. The current results are verified by illustrative examples.

scholarly journals On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Jorge Losada ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential ◽  
The Given

We introduce boundary value conditions involving antiperiodic and nonlocal three-point boundary conditions. We solve a nonlinear fractional differential equation supplemented with those conditions. We obtain some existence results for the given problem by applying some standard tools of fixed point theory. These results are well illustrated with the aid of examples.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

scholarly journals On solvability of some $ p $-Laplacian boundary value problems with Caputo fractional derivative

2021 ◽  
Vol 6 (12) ◽  
pp. 13622-13633
Author(s):  
Xiaoping Li ◽  
◽  
Dexin Chen ◽  
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Analysis Techniques

<abstract><p>The solvability of some $ p $-Laplace boundary value problems with Caputo fractional derivative are discussed. By using the fixed-point theory and analysis techniques, some existence results of one or three non-negative solutions are obtained. Two examples showed that the conditions used in this paper are somewhat easy to check.</p></abstract>

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