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Sign properties of Green’s functions for a family of two-point boundary value problems. (English) Zbl 0795.34010

Theorems defining the sign behaviour and giving comparison inequalities are proved for the Green functions of a family of two-point boundary value problems for the linear differential operator \(Ly= y^{(n)}+ a_ 1(x) y^{(n-1)}+ \cdots+ a_ n(x)y\). The results are then extended to a larger family of two-point boundary conditions. Assuming that \(L\) is left disfocal, the boundary conditions will first be stacked to the right end point and allowed to fan out at the left end point. Application in elastic beam problems is mentioned.
Reviewer: V.Burjan (Praha)

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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