scholarly journals Positive solutions of higher-order four-point boundary value problem with p-Laplacian operator

2010 ◽  
Vol 233 (11) ◽  
pp. 2757-2766 ◽  
Author(s):  
Hongyun Wu ◽  
Jihui Zhang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Order Four

scholarly journals Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongping Sun ◽  
Qian Sun ◽  
Xiaoping Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Functional Type ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Cone Expansion And Compression

This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.

scholarly journals Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with p-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective.

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.

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