linear integral operators
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Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 828 ◽  
Author(s):  
Yaohong Li ◽  
Jie Liu ◽  
Donal O’Regan ◽  
Jiafa Xu

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.


2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Juan Mao ◽  
Daliang Zhao

By using the theory of fixed-point index on cone for differentiable operators, spectral radii of some related linear integral operators, and properties of Green’s function, the existence of multiple positive solutions to a nonlinear fractional differential system with integral boundary value conditions and a parameter is established. At last, some examples are also provided to illustrate the validity of our main results.


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