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Multivalued linear operators and differential inclusions in Banach spaces

100%
Baskakov A., Obukhovskii V., Zecca P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2003
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tom 23
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nr 1
53-74
EN
In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued nonlinearities. As a consequence, we give theorems on the existence of local, global and bounded solutions of the Cauchy problem for degenerate differential inclusions.
2
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Qualitative behavior of a class of second order nonlinear differential equations on the halfline

100%
Staněk S.
Annales Polonici Mathematici
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1993
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tom 58
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nr 1
65-83
EN
A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
3
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On positive solutions of a class of second order nonlinear differential equations on the halfline

100%
Staněk S.
Annales Polonici Mathematici
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1995
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tom 62
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nr 2
123-142
EN
The differential equation of the form $(q(t)k(u)(u')^a)' = f(t)h(u)u'$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u'(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
4
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Nonnegative solutions of a class of second order nonlinear differential equations

100%
Staněk S.
Annales Polonici Mathematici
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1992
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tom 57
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nr 1
71-82
EN
A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.
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