Abstract
We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear periodic boundary value problems associated with second-order differential equations with a functional dependence, which is a piecewise constant function. Our analysis lies in the study of the sign of the Green’s function.
Highlights
Delay differential equations find interesting applications in fields like biology, fisiology, physics, etc
The existence of solutions with a constant sign is important from the point of view of the interpretation of the biological models
Recent work [8] deepens the problem of the existence of non-negative solutions to linear autonomous functional differential equations
Summary
Delay differential equations find interesting applications in fields like biology, fisiology, physics, etc. For s = 0 or s = T, the unique solution to problem (2) is non-negative if the following conditions hold: (i) h1 ≥ 0, h2 ≥ 0 on (0, 1); h10 ≥ 0, h20 ≥ 0 on (0, 1); h i −1 (iii) The elements in the second column of the matrix I − H ( T − [ T ]) C [T ]
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