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1
Content available remote Second order differential inequalities via aggregation
Herzog G., Lemmert R.
Demonstratio Mathematica
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2007
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Vol. 40, nr 2
347-364
EN
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.
2
Content available remote Numerical method of lines for first order partial differential equations with deviated variables
Czernous W.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
239--254
EN
Classical solutions of nonlinear initial boundary value problems are approximated in the paper by solutions of suitable quasilinear differential difference systems. The proof of the stability of the method of lines is based on a comparison technique with nonlinear estimates of the Perron type. Numerical examples are given.
3
Content available remote On-sided estimates for quasimonotone systems of boundary value problem
Herzog G.
Demonstratio Mathematica
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2004
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Vol. 37, nr 4
847--856
EN
We prove existence and uniqueness theorems for Dirichlet boundary value problems of the form u" + f(t,u) = 0, u(0) = uo, u(1) = ui in ordered finite dimensional Banach spaces, involving one-sided estimates and quasimonotonicity.
4
Content available remote Equipower and equichordal extension
Stępnicki R.
Demonstratio Mathematica
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2004
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Vol. 37, nr 4
925--938
EN
In this paper we consider the possibility of extension of a concave function f : [0, a] -> [0, +oo) to equipower convex curve or equichordal convex curve with axis of symmetry. The extension is possible if and only if f satisfies a differential inequality of the second degree.
5
Content available remote Stability of a new iteration method for strongly pseudocontractive mappings
Stević S.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
404--412
EN
In this note we prove that a recently introduced iteration procedure is almost stable with respect to strong pseudocontractions in real uniformly Banach spaces.
6
Content available remote Elliptic and parabolic differential inequalities
Buica A.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
782-792
7
Content available remote Relaxing constrained control systems
Frankowska H., Rampazzo F.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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Vol. 46, no 1
70-81
EN
In this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control. In particular we show that the Mangasarian-Fromowitz constraint qualification allows to rewrite constrained systems as differential inclusions with locally Lipschitz right-hand side. Then Filippov-Ważewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions. If, besided agreeing with the above constraints, the state has to remain in a control-independent set K, then we provide a condition on the feasible velocities on the boundary of K to get a relaxation theorem.
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