scholarly journals Multiple Positive Solutions for First-Order Impulsive Integrodifferential Equations on the Half Line in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Positive Solutions ◽  
Integrodifferential Equations ◽  
Half Line ◽  
Multiple Positive Solutions ◽  
First Order ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression ◽  
Infinite Boundary Value Problem

The author discusses the multiple positive solutions for an infinite boundary value problem of first-order impulsive superlinear integrodifferential equations on the half line in a Banach space by means of the fixed point theorem of cone expansion and compression with norm type.

scholarly journals Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Su ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
The Fixed Point Theorem

We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.

scholarly journals Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Huiqin Lu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
First Order ◽  
Periodic Boundary Value Problems ◽  
The Fixed Point Theorem ◽  
Special Cone

By constructing a special cone inC1[0,2π]and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. Further, an example is given to demonstrate the applications of our main results.

Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities

2020 ◽  
Vol 26 (2) ◽  
pp. 193-207
Author(s):  
Meryem Hellal ◽  
N. Merzagui
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
First Order ◽  
The Fixed Point Theorem

AbstractIn this work, we use the fixed-point theorem in double cones to study the existence of multiple positive solutions for an impulsive first-order differential system with integral boundary conditions, when the nonlinearities change sign.

scholarly journals Multiple Positive Solutions for Fractional Three-Point Boundary Value Problem with p-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Dong Li ◽  
Yang Liu ◽  
Chunli Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
The Fixed Point Theorem

In this paper, we investigate the existence of multiple positive solutions or at least one positive solution for fractional three-point boundary value problem with p-Laplacian operator. Our approach relies on the fixed point theorem on cones. The results obtained in this paper essentially improve and generalize some well-known results.

scholarly journals Positive solutions of nth-order impulsive differential equations with integral boundary conditions

2016 ◽  
Vol 24 (1) ◽  
pp. 243-261
Author(s):  
Fatma Tokmak Fen ◽  
Ilkay Yaslan Karaca
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Impulsive Differential Equations ◽  
Integral Boundary ◽  
Impulsive Boundary Value Problem ◽  
Existence And Nonexistence ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

AbstractThis paper is concerned with the existence and nonexistence of positive solutions of nth-order impulsive boundary value problem with integral boundary conditions. The fixed point theorem of cone expansion and compression is used to investigate the existence of at least one positive solution. Also, an example is given to illustrate the effective of our results.

scholarly journals Positive Solutions for a Nonlinear Higher Order Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yaohong Li ◽  
Haiyan Zhang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Higher Order ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

We investigate the existence of positive solutions for a nonlinear higher order differential system, where the differential system is coupled not only in the differential system but also through the boundary conditions. By constructing a special cone and using the fixed point theorem of cone expansion and compression of norm type, the existence of single and multiple positive solutions is established. As an application, we give some examples to demonstrate our results.

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