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
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.

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.