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Second order differential inequalities via aggregation

Herzog G., Lemmert R.

Demonstratio Mathematica

2007

Vol. 40, nr 2

347-364

Let E be a Banach space ordered by a solid and normal cone. We introduce a polynorm with respect to a given selection of positive pairwise disjoint vectors p1, . . . , pm, and derive monotonicity properties of solutions of second order differential inequalities under one-sided matrix Lipschitz conditions.

On bounded solutions of second order systems

Herzog G.

Demonstratio Mathematica

2006

Vol. 39, nr 4

793-801

We prove existence and uniqueness of bounded solutions of u"+f(t, u) = 0, u(0) = x on [0,infinity) under quasimonotonicity and one-sided Lipschitz conditions on f.