Topological Methods in Differential Equations (AN10)
Graduate Courses Outlines - Department of Mathematics
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 |
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. |
Syllabus
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