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Lecturer(s)
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Rachůnková Irena, prof. RNDr. DrSc.
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Vodák Rostislav, RNDr. Ph.D.
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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. Functional boundary value problems.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), 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.
Application Demonstrate a good orientation ín the theory of boundary value problems and in methods of their investigation.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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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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D. O'Regan. (1997). Existence Theory for Nonlinear Ordinary Differential Equations. Kluwer, Dordrecht.
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D. O'Regan. (1994). Theory of Singular Boundary Value Problems. World Scientific, Singapore.
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I.T. Kiguradze, B.L. Shekhter. (1987). Singular Boundary Value Problems for Ordinary Second Order Differential Equations. ) INT 30, Moscow.
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I.T. Kiguradze. (1987). Boundary Value Problems for Systems of Ordinary Differential Equations. INT 30, Moscow.
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N. I. Vasiljev, Ju. A. Klokov. (1978). Základy teorie okrajových úloh ODR. Zinatne, Riga.
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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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