Positive solutions of fractional p-Laplacian equations with integral boundary value and two parameters

AbstractWe consider a class of Caputo fractional p-Laplacian differential equations with integral boundary conditions which involve two parameters. By using the Avery–Peterson fixed point theorem, we obtain the existence of positive solutions for the boundary value problem. As an application, we present an example to illustrate our main result.

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POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2015.1020531 ◽

2015 ◽

Vol 20 (2) ◽

pp. 188-204 ◽

Cited By ~ 4

Author(s):

Ilkay Yaslan Karaca ◽

Fatma Tokmak Fen

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Positive Solutions ◽

Point Theorem ◽

Boundary Value ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

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Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2018-0038 ◽

2018 ◽

Vol 21 (3) ◽

pp. 716-745 ◽

Cited By ~ 5

Author(s):

Seshadev Padhi ◽

John R. Graef ◽

Smita Pati

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Positive Solutions ◽

Point Theorem ◽

Boundary Value ◽

Multiple Positive Solutions ◽

Integral Boundary ◽

Existence Of Positive Solutions

Abstract In this paper, we study the existence of positive solutions to the fractional boundary value problem $$\begin{array}{} \displaystyle D^{\alpha }_{0+}x(t)+q(t)f(t,x(t))=0, \,\, 0\lt t \lt1, \end{array}$$ together with the boundary conditions $$\begin{array}{} \displaystyle x(0)=x^{\prime}(0)= \cdots = x^{(n-2)}(0)=0, D_{0+}^{\beta }x(1)= \int^{1}_{0}h(s,x(s))\,dA(s), \end{array}$$ where n > 2, n – 1 < α ≤ n, β ∈ [1,α – 1], and $\begin{array}{} \displaystyle D^{\alpha }_{0+} \end{array}$ and $\begin{array}{} \displaystyle D^{\beta }_{0+} \end{array}$ are the standard Riemann-Liouville fractional derivatives of order α and β, respectively. We consider two different cases: f, h : [0, 1] × R → R, and f, h : [0, 1] × [0, ∞) → [0, ∞). In the first case, we prove the existence and uniqueness of the solutions of the above problem, and in the second case, we obtain sufficient conditions for the existence of positive solutions of the above problem. We apply a number of different techniques to obtain our results including Schauder’s fixed point theorem, the Leray-Schauder alternative, Krasnosel’skii’s cone expansion and compression theorem, and the Avery-Peterson fixed point theorem. The generality of the Riemann-Stieltjes boundary condition includes many problems studied in the literature. Examples are included to illustrate our findings.

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Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

Abstract and Applied Analysis ◽

10.1155/2014/602604 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Hongjie Liu ◽

Xiao Fu ◽

Liangping Qi

Keyword(s):

Fixed Point ◽

Green Function ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Positive Solutions ◽

Boundary Value ◽

Fractional Boundary Value Problem ◽

Existence Of Positive Solutions ◽

Liouville Fractional Derivative ◽

Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

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Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions

Journal of Function Spaces ◽

10.1155/2016/3805804 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12

Author(s):

Jian Chang ◽

Jian-Ping Sun ◽

Ya-Hong Zhao

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Positive Solutions ◽

Integral Boundary Conditions ◽

Multiple Positive Solutions ◽

Stieltjes Integral ◽

Integral Conditions ◽

Third Order ◽

Integral Boundary

We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions:u′′′t+ft,uαt=0, t∈0,1, u0=γuη1+λ1uandu′′0=0, u1=βuη2+λ2u, where0<η1<η2<1,0≤γ,β≤1,α:[0,1]→[0,1]is continuous,α(t)≥tfort∈[0,1], andα(t)≤η2fort∈[η1,η2]. Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained.

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Existence of positive solutions of Neumann boundary value problem via a cone compression-expansion fixed point theorem of functional type

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-009-0360-4 ◽

2009 ◽

Vol 35 (1-2) ◽

pp. 341-349 ◽

Cited By ~ 5

Author(s):

Feng Wang ◽

Fang Zhang

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Positive Solutions ◽

Point Theorem ◽

Boundary Value ◽

Neumann Boundary ◽

Functional Type ◽

Neumann Boundary Value Problem ◽

Existence Of Positive Solutions

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Positive solutions for singular semipositone nonlinear fractional differential system

Filomat ◽

10.2298/fil2101169b ◽

2021 ◽

Vol 35 (1) ◽

pp. 169-179

Author(s):

Rim Bourguiba ◽

Faten Toumi

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Positive Solutions ◽

Fractional Differential Equations ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Fractional Differential System ◽

Nonlinear Alternative ◽

Existence Of Positive Solutions ◽

Fractional Differential

In this paper, under suitable conditions we employ the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel?skii fixed point theorem to show the existence of positive solutions for a system of nonlinear singular Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. Some examples are given to illustrate our main results.

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Existence of positive solutions for second-order undamped Sturm–Liouville boundary value problems

Asian-European Journal of Mathematics ◽

10.1142/s1793557116500893 ◽

2016 ◽

Vol 09 (04) ◽

pp. 1650089 ◽

Cited By ~ 1

Author(s):

K. R. Prasad ◽

L. T. Wesen ◽

N. Sreedhar

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Positive Solutions ◽

Boundary Value ◽

Second Order ◽

Multiple Positive Solutions ◽

Second Order Differential Equations ◽

Existence Of Positive Solutions ◽

Sturm Liouville

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

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Existence of positive solutions of Hadamard fractional defferential equations with integral boundary conditions

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.44099 ◽

2022 ◽

Vol 40 ◽

pp. 1-14

Author(s):

Berhail Amel ◽

Nora Tabouche

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Positive Solutions ◽

Fractional Differential Equations ◽

Integral Boundary Conditions ◽

Integral Conditions ◽

Integral Boundary ◽

Hadamard Fractional Differential Equations ◽

Existence Of Positive Solutions ◽

Fractional Differential

In this paper, We study the existence of positive solutions for Hadamard fractional differential equations with integral conditions. We employ Avery-Peterson fixed point theorem and properties of Green's function to show the existence of positive solutions of our problem. Furthermore, we present an example to illustrate our main result.

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Positive solutions of impulsive time-scale boundary value problems with p-Laplacian on the half-line

Filomat ◽

10.2298/fil1902415y ◽

2019 ◽

Vol 33 (2) ◽

pp. 415-433

Author(s):

Karaca Yaslan ◽

Aycan Sinanoglu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Value Problems ◽

Positive Solutions ◽

Time Scale ◽

Boundary Value ◽

Dynamic Equations ◽

Half Line ◽

Existence Of Positive Solutions

In this paper, four functionals fixed point theorem is used to investigate the existence of positive solutions for second-order time-scale boundary value problem of impulsive dynamic equations on the half-line.

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