Abstract
We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. MSC:34A08, 45G15.
Highlights
We consider the system of nonlinear ordinary fractional differential equations (S)with the integral boundary conditions u( ) = u ( ) = · · · = u(n– )( ) =, v( ) = v ( ) = · · · = v(m– )( ) =, u( ) =u(s) dH (s), v( ) = v(s) dK (s), (BC)where n, m ∈ N, n, m ≥, Dα +, and Dβ + denote the Riemann-Liouville derivatives of orders α and β, respectively, the integrals from (BC) are Riemann-Stieltjes integrals and f, g are sign-changing continuous functions
We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions
1 Introduction We consider the system of nonlinear ordinary fractional differential equations
Summary
Where n, m ∈ N, n, m ≥ , Dα +, and Dβ + denote the Riemann-Liouville derivatives of orders α and β, respectively, the integrals from (BC) are Riemann-Stieltjes integrals and f , g are sign-changing continuous functions (that is, we have a so-called system of semipositone boundary value problems). In [ ], the authors obtained the existence and multiplicity of positive solutions (u(t) ≥ , v(t) ≥ for all t ∈ [ , ], supt∈[ , ] u(t) > , supt∈[ , ] v(t) > ) by applying some theorems from the fixed point index theory. We would like to mention the paper [ ], where the authors investigated the existence and multiplicity of positive solutions of the semipositone system (S) with α = β and the boundary conditions u(i)( ) = v(i)( ) = , i = , .
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.
