Abstract
This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows ( p − 1 ) -superlinearly and ( p − 1 ) -sublinearly, the existence of positive solutions is obtained via fixed point index. Moreover, using an increasing operator fixed-point theorem, the uniqueness of positive solutions and uniform convergence sequences are also established.
Highlights
Yang in [53] used the comparison principle and the monotone iterative technique combined with the subsolution and supersolution method to study the existence of extremal solutions for Hadamard fractional differential equations with Cauchy initial value conditions
We study the existence of positive solutions for the Hadamard fractional p-Laplacian three-point boundary value problem [1]
We only provide the definition for the Hadamard fractional derivative; for more details about Hadamard fractional calculus, see the book [73]
Summary
We study the existence and uniqueness of positive solutions for the Hadamard fractional p-Laplacian three-point boundary value problem In [3], the authors adopted some fixed-point theorems on cones to study the unique solution for the fractional p-Laplacian boundary value problem β. Yang in [53] used the comparison principle and the monotone iterative technique combined with the subsolution and supersolution method to study the existence of extremal solutions for Hadamard fractional differential equations with Cauchy initial value conditions. In [54], the authors used fixed point methods to study the existence of positive solutions for Hadamard fractional integral boundary value problems. We study the existence of positive solutions for the Hadamard fractional p-Laplacian three-point boundary value problem [1]. Note: (i) we establish some relations from the corresponding problem without the p-Laplacian operator, and use some ( p − 1)-superlinearly and ( p − 1)-sublinearly conditions for the nonlinearity to obtain positive solutions for [1]; (ii) using an increasing operator fixed-point theorem, we obtain the unique solution for [1], and establish uniformconverged sequences for this solution
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
