Existence of positive solutions for a system of Caputo fractional difference equations depending on parameters

• Published in: Advances in difference equations Vol. 2015; no. 1; pp. 1 - 14
• Main Authors: Kang, Shugui, Chen, Huiqin, Guo, Jianmin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 06.05.2015; Springer Nature B.V
• Subjects: Analysis; Boundary conditions; Boundary value problems; Difference and Functional Equations; Difference equations; Existence theorems; Functional Analysis; Mathematical analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Texts; Theorems; Caputo fractional difference; positive solution; fixed point theory; 39A12; 26A33; 39A05; boundary value problem
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-015-0466-y

We consider the existence of at least two positive solutions for a system of Caputo fractional difference equations Δ C ν j y j ( t ) = − λ j f j ( y 1 ( t + ν 1 − 1 ) , … , y n ( t + ν n − 1 ) ) , subject to boundary conditions y j ( ν j − 3 ) = Δ y j ( ν j + b ) = Δ 2 y j ( ν j − 3 ) = 0 , where 2 < ν j ⩽ 3 , j = 1 , … , n . We use the Krasnosel’skiĭ fixed point theorem to obtain the sufficient conditions of the existence of two positive solutions for this boundary value problem of Caputo fractional difference equations depending on parameters.