scholarly journals Multiplicity of Positive Solutions to Nonlocal Boundary Value Problems with Strong Singularity

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 7
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Index Theory ◽  
Open Interval ◽  
Nonlocal Boundary Conditions ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions ◽  
The Given

In this paper, we consider generalized Laplacian problems with nonlocal boundary conditions and a singular weight, which may not be integrable. The existence of two positive solutions to the given problem for parameter λ belonging to some open interval is shown. Our approach is based on the fixed point index theory.

scholarly journals Positive Solutions for Nonlinearq-Fractional Difference Eigenvalue Problem with Nonlocal Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Wafa Shammakh ◽  
Maryam Al-Yami
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Index Theory ◽  
Nonlocal Boundary Conditions ◽  
Fractional Difference ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The problem of positive solutions for nonlinearq-fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem.

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 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 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.

Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity

2010 ◽  
Vol 140 (6) ◽  
pp. 1187-1196
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Image Position

We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.

scholarly journals Positive solutions of singular nonlinear Sturm-Liouville boundary value problems

2004 ◽  
Vol 45 (4) ◽  
pp. 557-571
Author(s):  
Yan Sun ◽  
Lishan Liu ◽  
Yeol Je Cho
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractBy using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

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