| Academic Year |
2026Year |
School/Graduate School |
School of Science |
| Lecture Code |
HX205900 |
Subject Classification |
Specialized Education |
| Subject Name |
数学特別講義（非線形二点境界値問題の基礎理論） |
Subject Name
（Katakana） |
スウガクトクベツコウギ（ヒセンケイニテンキョウカイチモンダイノキソリロン） |
Subject Name in
English |
Special Lectures in Mathematics(Fundamental theory of nonlinear two-point boundary value problems) |
| Instructor |
To be announced.,NAITO YUKI |
Instructor
(Katakana) |
タントウキョウインミテイ,ナイトウ ユウキ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, Second Semester, Second Semester |
| Days, Periods, and Classrooms |
(2nd) Inte |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| |
| Credits |
1.0 |
Class Hours/Week |
|
Language of Instruction |
B
:
Japanese／English |
| Course Level |
4
:
Undergraduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
4th-Year, Second Semester |
| Keywords |
Boundary value problems, Fractional derivatives, Order topology, Krein-Rutman theorem |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
This course provides an introduction to nonlinear two-point boundary value problems with fractional derivatives, a field that has seen rapid theoretical advancement and active discussion in recent years. Students will first master the construction of Green's functions and the fundamental concepts of the order topology. Building on this foundation, the course explores the properties of the first eigenvalue through the Krein-Rutman theorem, systematically examining the mechanisms that determine the existence, non-existence, uniqueness, and multiplicity of positive solutions. The ultimate goal is for students to acquire the analytical techniques necessary to logically elucidate the solution structures of nonlinear boundary value problems. |
| Class Schedule |
1. Introduction to the problems addressed in this course and explanation of Green's functions.
2. Introduction to the concepts of the order topology.
3. Introduction to the Krein-Rutman theorem and demonstration of the properties of the first eigenvalue.
4. Demonstration of the existence and non-existence of positive solutions.
5. Demonstration of the uniqueness and multiplicity of positive solutions.
|
Text/Reference
Books,etc. |
No textbook is required and lecture materials will be distributed. This course is based on the following paper:
Inbo Sim and Satoshi Tanaka, Positive solutions for fractional-order boundary value problems with or without dependence of integer-order ones, Fract. Calc. Appl. Anal. 29 (2026), no. 1, 66–100.
The following is a reference for the order topology and the Krein-Rutman theorem:
Klaus Deimling, Nonlinear Functional Analysis (Dover Books on Mathematics), 2010.
|
PC or AV used in
Class,etc. |
Text |
| (More Details) |
|
| Learning techniques to be incorporated |
Post-class Report |
Suggestions on
Preparation and
Review |
Students are encouraged to review using the distributed materials. Questions regarding the lecture content are welcome.
|
| Requirements |
|
| Grading Method |
Evaluation will be based on the assessment of submitted reports. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |