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On monotone-like mappings in Orlicz-Sobolev spaces

Vesa Mustonen, Matti Tienari (1999)

Mathematica Bohemica

We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class ( S m ) as a generalization of ( S + ) and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.

On solvability of nonlinear operator equations and eigenvalues of homogeneous operators

Věra Burýšková, Slavomír Burýšek (1996)

Mathematica Bohemica

Notions as the numerical range W ( S , T ) and the spectrum ( S , T ) of couple ( S , T ) of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation S x - l T x = y . Conditions for the existence of eigenvalues of the couple ( S , T ) are given.

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

Andrzej Nowakowski, Aleksandra Orpel (2006)

Czechoslovak Mathematical Journal

The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.

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