Topological Methods in Differential Equations (AN10)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | AN10 |
| Semester | 2 |
| Course Title | Topological Methods in Differential Equations |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Specialized general knowledge |
| Prerequisite Courses | Differential Equations, General Topology, Functional Analysis, Real Analysis |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students | Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
Knowledge of topics in functional analysis with application in differential equations. Ability to start research in problems related to qualitative theory of differential equations. Become familiar with research bibliography concerning qualitative theory in a wide sector of differential equations. |
|---|---|
| General Competences |
Search for, analysis and synthesis of data and information, with the use of the necessary technology. Production of new research ideas. Contact research bibliography concerning qualitative theory in a wide sector of differential equations. |
Syllabus
Application of topological fixed point theorems in the theory of differential equations, contraction theorems, theorems of Schauder, Schaefer, degree theory, nonlinear alternative, fixed point theorems in cones, Krasnoselskii’s theorems, theorems of Leggett-Williams type. Applications in initial value and boundary value problems, in integro-differential equations and functional differential equations. Existence of solutions, of positive solutions, of upper and lower solutions.
Teaching and Learning Methods - Evaluation
| Delivery |
Face to face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Problem solving, written work, essay/report, oral or/and written examination, public presentation. |
Attached Bibliography
- H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, No. 4 ,1976 (pages 620-709)
- K. Deimling, Nonlinear functional analysis, Springer-Verlag, New York,1985
- R. D. Driver, Ordinary and delay differential equations, Springer Verlag, New York, 1976
- D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones, Academic Press, San Diego,1988
- J. K. Hale and S. M. V. Lunel, Introduction to functional differential equations, Springer Verlag, New York, 1993.