scholarly journals Multiplicity of Positive Solutions for Fractional Differential Equation withp-Laplacian Boundary Value Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Fixed Integer ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence of multiple positive solutions of fractional differential equations withp-Laplacian operatorDa+β(ϕp(Da+αu(t)))=f(t,u(t)),  a<t<b,uja=0,  j=0,1,2,…,n-2,u(α1)(b)=ξu(α1)(η),ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), whereβ∈(1,2],α∈(n-1,n],  n≥3,ξ∈(0,∞),η∈(a,b),β1∈(0,1],α1∈{1,2,…,α-2}is a fixed integer, andϕp(s)=|s|p-2s,  p>1,  ϕp-1=ϕq,  (1/p)+(1/q)=1, by applying Leggett–Williams fixed point theorems and fixed point index theory.

scholarly journals Multiple Positive Solutions for a System of Nonlinear Caputo-Type Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Fractional Differential

By using fixed-point index theory, we consider the existence of multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations with the Riemann-Stieltjes boundary conditions.

scholarly journals Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem forp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Francisco J. Torres
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Main Tool ◽  
Index Theory ◽  
Laplacian Operator ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

The author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation withp-Laplacian operator. The main tool is fixed point index theory and Leggett-Williams fixed point theorem.

Positive Solutions for a Semipositone Singular Riemann–Liouville Fractional Differential Problem

2019 ◽  
Vol 20 (7-8) ◽  
pp. 823-831 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Rodica Luca
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Differential Problem ◽  
Height Functions ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Bounded Sets

AbstractWe study the existence of multiple positive solutions for a nonlinear singular Riemann–Liouville fractional differential equation with sign-changing nonlinearity, subject to Riemann–Stieltjes boundary conditions which contain fractional derivatives. In the proof of our main theorem, we use various height functions of the nonlinearity of equation defined on special bounded sets, and two theorems from the fixed point index theory.

scholarly journals Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3931-3942
Author(s):  
Rodica Luca
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Index Theory ◽  
Point Index ◽  
Differential Problem ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence and multiplicity of positive solutions for a nonlinear Riemann-Liouville fractional differential equation with a nonnegative singular nonlinearity, subject to Riemann-Stieltjes boundary conditions which contain fractional derivatives. In the proofs of our main results, we use an application of the Krein-Rutman theorem and some theorems from the fixed point index theory.

scholarly journals On a singular Riemann–Liouville fractional boundary value problem with parameters

2021 ◽  
Vol 26 (1) ◽  
pp. 151-168
Author(s):  
Alexandru Tudorache ◽  
Rodica Luca
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Index Theory ◽  
Nonlocal Boundary Conditions ◽  
Principal Characteristic ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Semipositone Problem ◽  
Fractional Differential

We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

scholarly journals Existence, Nonexistence and Multiplicity of Positive Solutions for Singular Boundary Value Problems Involving φ-Laplacian

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 953 ◽  
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Interesting Point ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.

scholarly journals Eigenvalue of Coupled Systems for Hammerstein Integral Equation with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wanjun Li
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Coupled Systems ◽  
Point Index ◽  
Hammerstein Integral Equation ◽  
Fixed Point Index Theory ◽  
Two Parameters

By using the fixed-point index theory, we discuss the existence, multiplicity, and nonexistence of positive solutions for the coupled systems of Hammerstein integral equation with parameters.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

scholarly journals Multiple positive solutions for a system of $(p_{1}, p_{2}, p_{3})$-Laplacian Hadamard fractional order BVP with parameters

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabbavarapu Nageswara Rao ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this article, we are pleased to investigate multiple positive solutions for a system of Hadamard fractional differential equations with $(p_{1}, p_{2}, p_{3})$ ( p 1 , p 2 , p 3 ) -Laplacian operator. The main results rely on the standard tools of different fixed point theorems. Finally, we demonstrate the application of the obtained results with the aid of examples.

Sign in / Sign up

Export Citation Format

Share Document