František Tumajer (1986)
Aplikace matematiky
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In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
Michal Fečkan (1992)
Mathematica Slovaca
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M. Altman (1970)
Fundamenta Mathematicae
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Lech Pasicki (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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The paper contains a fixed point theorem for stable mappings in metric discus spaces (Theorem 10). A consequence is Theorem 11 which is a far-reaching extension of the fundamental result of Browder, Göhde and Kirk for non-expansive mappings.
Michal Fečkan (1991)
Mathematica Slovaca
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Alexander Shnirelman (1999-2000)
Séminaire Équations aux dérivées partielles
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Naresh Kumar Dua, Hari Kishan, Ruchi Goel (2011)
Annales Polonici Mathematici
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The hydromagnetic stability of stratified shear flows in the presence of cross flows is discussed. The magnetic field is applied in the direction of the main flow. Some necessary conditions of instability, the growth rate of unstable modes and reduction of the unstable region are discussed.