A complete algebraic solvability test for the nonstrict Lyapunov inequality

1995 ◽  
Vol 25 (5) ◽  
pp. 327-335 ◽  
Author(s):  
Carsten W. Scherer
Keyword(s):  
Lyapunov Inequality ◽  
Algebraic Solvability

Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem

2019 ◽  
Vol 22 (3) ◽  
pp. 750-766 ◽  
Author(s):  
Xiangyun Meng ◽  
Martin Stynes
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Problem ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Lyapunov Inequality ◽  
Nonlinear Boundary Problem

Abstract We consider a nonlinear boundary problem whose highest-order derivative is a Caputo derivative of order α with 1 < α < 2. Properties of its associated Green’s function are derived. These properties enable us to deduce sufficient conditions for the existence of a positive solution to the boundary value problem and to prove a Lyapunov inequality for the problem. Our results sharpen and extend earlier results of other authors.

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