Positive solutions for three-point boundary value problem of fractional differential equation with \(p\)-Laplacian operator
type: Item
instance of: scholarly article
title: Positive solutions for three-point boundary value problem of fractional differential equation with \(p\)-Laplacian operator
zbMATH Open document ID: 1267.35245
DOI: 10.1155/2013/376938
author: Shang-lin Yao
author: Guohui Wang
author: Zhiping Li
author: Li-jun Yu
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with \(p\)-Laplacian operator \(-\mathcal D^\beta_{\mathbf{t}}(\varphi_p(\mathcal D^\alpha_{\mathbf{t}}x))(t) = h(t)f(t, x(t)), t \in (0, 1), x(0) = 0, \mathcal D^\gamma_{\mathbf{t}}x(1) = a\mathcal D^\gamma_{\mathbf{t}}x(\xi), \mathcal D^\alpha_{\mathbf{t}}x(0) = 0\), where \(\mathcal D^\beta_{\mathbf{t}}, \mathcal D^\alpha_{\mathbf{t}}, \mathcal D^\gamma_{\mathbf{t}}\) are the standard Riemann-Liouville derivatives with \(1 < \alpha \leq 2, 0 < \beta \leq 1, 0 < \gamma \leq 1, 0 \leq \alpha - \gamma- 1, \xi \in (0, 1)\) and the constant \(a\) is a positive number satisfying \(a\xi^{\alpha-\gamma-2} \leq 1 - \gamma\); \(p\)-Laplacian operator is defined as \(\varphi_p(s) = |s|^{p-2}s\), \(p > 1\). By applying monotone iterative technique, some sufficient conditions for the existence of multiple positive solutions are established; moreover iterative schemes for approximating these solutions are also obtained, which start off a known simple linear function. In the end, an example is worked out to illustrate our main results.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6175073
Wikidata QID: Q58921538
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/376938
OpenAlex ID: W2004450472
cites work: Existence of positive solutions of nonlinear fractional differential equations
cites work: Existence and uniqueness for a nonlinear fractional differential equation
cites work: Nonlinear functional differential equations of arbitrary orders
cites work: Theory of fractional functional differential equations
cites work: Existence of positive solution for some class of nonlinear fractional differential equations
cites work: Existence and uniqueness of fractional functional differential equations with unbounded delay
cites work: Positive solutions for boundary value problem of nonlinear fractional differential equation
cites work: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations
cites work: Positive solutions for third-order Sturm-Liouville boundary value problems with \(p\)-Laplacian
cites work: Upper and lower solutions method for a class of singular fractional boundary value problems with \(p\)-Laplacian operator
cites work: Positive solutions for boundary value problem of fractional differential equation with \(p\)-Laplacian operator
description: scientific article; zbMATH DE number 6175073