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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Andres Jan, prof. RNDr. dr hab. DSc.
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Rachůnková Irena, prof. RNDr. DrSc.
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Course content
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Boundary conditions for ordinary differential equations. Classical and Carathéodory theory. Operator forms of boundary value problems. Green functions. Resonance. Fredholm operators. Fixed point theorems and their application. A priori estimates of solutions. Lower and upper functions method. Topological degree. Generalized inversion. Leray-Schauder type theorems. Impulsive boundary value problems. Boundary value problems with singularities in time variable and in phase variables.
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Learning activities and teaching methods
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Work with Text (with Book, Textbook)
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Learning outcomes
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Master given tools of the functional analysis, topology, theory of differential equations and dynamical systems for investigation of boundary value problems.
Knowledge Gain useful knowledge about theory boundary value problems for ODEs.
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Prerequisites
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Master degree in mathematics
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Assessment methods and criteria
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Oral exam
Oral exam.
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Recommended literature
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Aktuální odborné články v mezinárodních matematických časopisech.
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A.Granas, R.B. Guenther, J. Lee. (1985). Nonlinear Boundary Value Problems for Ordinary Differential Equations. Polish Scientific Publ. Warszawa.
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A.Granas, R.B. Guenther, J. Lee. Some General Existence Principles in the Catathéodory Theory of Nonlinear Differential Systems. J. Math. Pures et appl. 70 (1991), 153-196.
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C. de Coster, P. Habets. (2006). Two-Point Boundary Value Problems Lower and Upper Solutions. Elsevier, Amsterdam.
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D. O'Regan. (1994). Theory of Singular Boundary Value Problems. World Scientific, Singapore.
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S. A. Wirkus, R. J. Swift, R. Szypowski. (2016). A Course in Differential Equations with Boundary-Value Problems. Taylor&Francis, Inc.
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S. Fučík, A.Kufner. (1978). Nelineární diferenciální rovnice. SNTL, Praha.
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S. Fučík. (1980). Solvability of Nonlinear Equations and Boundary Value Problems. JČMF.
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