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	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	Activity Semester Workload Lectures, seminars 45 Exercises, Projects 52.5 Personal study 90 Course total 187.5
Student Performance Evaluation	Problem solving, written work, essay/report, oral or/and written examination, public presentation.