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A theorem of the Hahn-Banach type and its applications

Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor (1992)

Annales Polonici Mathematici

Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.

A third order boundary value problem subject to nonlinear boundary conditions

Gennaro Infante, Paolamaria Pietramala (2010)

Mathematica Bohemica

Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.

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