scholarly journals Multiplicity Results for Positive Solutions to Differential Systems of Singular Coupled Integral Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yujun Cui
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Integral Boundary ◽  
Differential Systems ◽  
Multiplicity Results ◽  
Integral Boundary Value Problems ◽  
Special Cone

By constructing a special cone and using a fixed-point theorem in cone, this paper investigates the existence of multiple solutions of coupled integral boundary value problems for a nonlinear singular differential system.

scholarly journals Existence Results for Fractional Hahn Difference and Fractional Hahn Integral Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Hahn Integral

The existence and uniqueness results of two fractional Hahn difference boundary value problems are studied. The first problem is a Riemann-Liouville fractional Hahn difference boundary value problem for fractional Hahn integrodifference equations. The second is a fractional Hahn integral boundary value problem for Caputo fractional Hahn difference equations. The Banach fixed-point theorem and the Schauder fixed-point theorem are used as tools to prove the existence and uniqueness of solution of the problems.

scholarly journals Multiple positive solutions of Strum-Liouville equations with singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Zenggui Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity

The existence of multiple positive solutions for Strum-Liouville boundary value problems with singularities is investigated. By applying a fixed point theorem of cone map, some existence and multiplicity results of positive solutions are derived. Our results improve and generalize those in some well-known results.

scholarly journals Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 970
Author(s):  
Youzheng Ding ◽  
Jiafa Xu ◽  
Zhengqing Fu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Integral ◽  
Matrix Theory ◽  
Boundary Value ◽  
Liouville Type ◽  
Integral Boundary ◽  
Integral Boundary Value Problems ◽  
Fractional Boundary Value Problems

In this work by the index of fixed point and matrix theory, we discuss the positive solutions for the system of Riemann–Liouville type fractional boundary value problems D 0 + α u ( t ) + f 1 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α v ( t ) + f 2 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α w ( t ) + f 3 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = u ′ ( 0 ) = ⋯ = u ( n − 2 ) ( 0 ) = 0 , D 0 + p u ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q u ( t ) d t , v ( 0 ) = v ′ ( 0 ) = ⋯ = v ( n − 2 ) ( 0 ) = 0 , D 0 + p v ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q v ( t ) d t , w ( 0 ) = w ′ ( 0 ) = ⋯ = w ( n − 2 ) ( 0 ) = 0 , D 0 + p w ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q w ( t ) d t , where α ∈ ( n − 1 , n ] with n ∈ N , n ≥ 3 , p , q ∈ R with p ∈ [ 1 , n − 2 ] , q ∈ [ 0 , p ] , D 0 + α is the α order Riemann–Liouville type fractional derivative, and f i ( i = 1 , 2 , 3 ) ∈ C ( [ 0 , 1 ] × R + × R + × R + , R ) are semipositone nonlinearities.

scholarly journals Multiple Solutions to Fractional Difference Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Huiqin Chen ◽  
Yaqiong Cui ◽  
Xianglan Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Fractional Difference ◽  
Schäuder Fixed Point Theorem

The following fractional difference boundary value problems▵νyt=-ft+ν-1,yt+ν-1,y(ν-2)=y(ν+b+1)=0are considered, where1<ν≤2is a real number and▵νy(t)is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions onfwhich are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results.

scholarly journals MULTIPLE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER DIFFERENCE EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 1-11
Author(s):  
DA-BIN WANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Multiple Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Order Difference ◽  
First Order ◽  
Periodic Boundary Value Problems

AbstractIn this paper, existence criteria for multiple solutions of periodic boundary value problems for the first-order difference equation are established by using the Leggett–Williams multiple fixed point theorem and fixed point theorem of cone expansion and compression. Two examples are also given to illustrate the main results.

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.

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