Positive solutions for a system of Riemann–Liouville fractional boundary value problems with p-Laplacian operators

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 30
• Main Authors: Tudorache, Alexandru, Luca, Rodica
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary conditions; Boundary value problems; Difference and Functional Equations; Differential equations; Existence of solutions; Existence theorems; Fixed points (mathematics); Functional Analysis; Mathematics; Mathematics and Statistics; Nonexistence of solutions; Nonlocal coupled boundary conditions; Nonnegative nonlinearities; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; Systems of Riemann–Liouville fractional differential equations; Nonexistence of solutions; 34B15; 34B10; Nonnegative nonlinearities; Systems of Riemann–Liouville fractional differential equations; Existence of solutions; Nonlocal coupled boundary conditions; 34A08; 34B18; 45G15
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02750-6

We study the existence and nonexistence of positive solutions for a system of Riemann–Liouville fractional differential equations with p -Laplacian operators, nonnegative nonlinearities and positive parameters, subject to coupled nonlocal boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. We use the Guo–Krasnosel’skii fixed point theorem in the proof of the main existence results.