Research

Research Interest

• A study on the qualitative properties of solutions to ordinary differential equations and difference equations

Keywords

• Oscillation Theory

• Ordinary Differential Equations

• Difference Equations

• Mathieu Equation, Whittaker-Hill Equation, Hill Equation

• Half-Linear Differential Equations

• Dynamic Equations on Time Scale

• Conformable Differential and Difference Equations, Proportional-derivative controller

Research grants

• 2026-2029, JSPS KAKENHI Grant-in-Aid for Scientific Research(C)

• 2024-2026, Grant for Basic Science Research Projects from The Sumitomo Foundation No. 2402156

• 2022-2025, JSPS KAKENHI Grant-in-Aid for Early-Career Scientists

Papers

1. K. Ishibashi and S. Shirakusa, A note on the linearized oscillation theorem for nonlinear RLC circuits of Duffing oscillator type, Acta Applicandae Mathematicae, Springer, 202 (2026), article number 6. [SJR]

2. K. Ishibashi, Wintner-type asymptotic behavior of linear differential systems with a proportional derivative controller, Opuscula Mathematica, 46, No. 1 (2026), 41-54. [SJR]

3. K. Ishibashi and M. Onitsuka, Oscillation criteria of the Leighton–Wintner-type and the Hille–Kneser-type for linear differential equations with a proportional derivative controller, Mathematical Methods in the Applied Sciences, John Wiley & Sons, 48 (2025), 16690-16699. [SJR]

4. K. Ishibashi, S. Miyauchi and H. Sakikawa, Oscillation of generalized Riemann–Weber type differential equations with delay, Results in Applied Mathematics, Elsevier, 27 (2025), Paper No.100637, 6 pp. [SJR]

5. K. Fujimoto, K. Ishibashi and M. Onitsuka, Leighton–Wintner-type oscillation theorem for the discrete p(k)-Laplacian, Applied Mathematics Letters, Elsevier, 163 (2025), Paper No. 109465, 6 pp. [SJR]

6. K. Ishibashi, Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales, Results in Applied Mathematics, Elsevier, 25 (2025), Paper No. 100553, 10 pp. [SJR]

7. K. Ishibashi, Partially extended oscillation and nonoscillation theorems for half-linear Hill-type differential equations with periodic damping, Mathematical Methods in the Applied Sciences, John Wiley & Sons, 48 (2025), 3748-3758. [SJR]

8. K. Ishibashi, Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations, Opuscula Mathematica, 44, No. 5 (2024), 727-748. [SJR]

9. J. Sugie and K. Ishibashi, The only limit cycle that appears in damped harmonic oscillators affected by state-dependent impulses, Journal of Mathematical Analysis and Applications, Elsevier, 531 (2024), Paper No. 127886, 26 pp. [SJR]

10. K. Ishibashi, Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations, Opuscula Mathematica, 43, No. 1 (2023), 67-79. [SJR]

11. K. Ishibashi, Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker-Hill-type equation, Monatshefte für Mathematik, Springer, 198 (2022), 741-756. [SJR]

12. K. Ishibashi, Nonoscillation criteria for damped half-linear dynamic equations with mixed derivatives on a time scale, Journal of Mathematical Analysis and Applications, Elsevier, 512 (2022), Paper No. 126183, 20 pp. [SJR]

13. J. Sugie and K. Ishibashi, Limit cycles of a class of Liénard systems derived from state-dependent impulses, Nonlinear Analysis: Hybrid Systems, Elsevier, 45 (2022), Paper No. 101188, 16 pp. [SJR]

14. K. Ishibashi, Non-oscillation criterion for generalized Mathieu-type differential equations with bounded coefficients, Proceedings of the American Mathematical Society, American Mathematical Society, 150 (2022), 231-244. [SJR]

15. K. Ishibashi, Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale, Electronic Journal of Differential Equations, 2021, No. 78 (2021), 1-15. [SJR]

16. F. Wu, L. She and K. Ishibashi, Moore-type nonoscillation criteria for half-linear difference equations, Monatshefte für Mathematik, Springer, 194 (2021), 377-393. [SJR]

17. J. Sugie and K. Ishibashi, Nonoscillation of Mathieu equations with two frequencies, Applied Mathematics and Computation, Elsevier, 346 (2019), 491-499. [SJR]

18. J. Sugie and K. Ishibashi, Oscillation problems for Hill's equation with periodic damping, Journal of Mathematical Analysis and Applications, Elsevier, 466 (2018), 56-70. [SJR]

19. J. Sugie and K. Ishibashi, Integral condition for oscillation of half-linear differential equations with damping, Applied Mathematics Letters, Elsevier, 79 (2018), 146-154. [SJR]

20. K. Ishibashi and J. Sugie, Simple conditions for parametrically excited oscillations of generalized Mathieu equations, Journal of Mathematical Analysis and Applications, Elsevier, 446 (2017), 233-247. [SJR]

Misc.

1. K. Ishibashi, Non-oscillation criteria for damped half-linear dynamic equations with mixed derivatives on a time scale, The 18th Mathematics Conference for Young Researchers : MCYR18, Hokkaido University technical report series in Mathematics, 182 (2022), 499-508.

2. K. Ishibashi, Nonoscillation of half-linear dynamic equations with mixed derivatives, Recent trends in ordinary differential equations and their developments, RIMS Kôkyûroku 2149 (2020), 1-13. 

3. K. Ishibashi, Nonoscillation of quasi-periodic Mathieu equations with two frequencies, Qualitative theory of ordinary differential equations and related areas, RIMS Kôkyûroku 2032 (2017), 21-33. 

Review

1. Zbl 08139094 zbMATH Open Review, January 29, 2026

2. Zbl 08107310 zbMATH Open Review, November 4, 2025

3. MR4555638 Mathematical Review, November 3, 2025

4. Zbl 07916589 zbMATH Open Review, February 6, 2025

5. Zbl 07729722 zbMATH Open Review, December 20, 2023

6. MR4555638 Mathematical Review, November 3, 2023

7. MR4418746 Mathematical Review, October 30, 2023

8. Zbl 07557561 zbMATH Open Review, November 28, 2022

9. MR4419101 Mathematical Review, September 21, 2022

10. MR4068077 Mathematical Review, September 21, 2022

11. Zbl 07513219 zbMATH Open Review, July 15, 2022

12. MR4330450 Mathematical Review, April 19, 2022

13. Zbl 07420397 zbMATH Open Review, January 14, 2022

14. MR4157593 Mathematical Review, June 30, 2021

Presentation (International Research Meetings)

1. K. Ishibashi, Nonoscillation of damped linear conformable differential equations, RIMS Workshop: Recent Development of Qualitative Theory on ODEs and its Applications, Kyoto University, October 25, 2023 (Invited Lecture). 

2. K. Ishibashi, Nonoscillation of half-linear dynamic equations with mixed derivatives, RIMS Workshop: Recent Trends in Ordinary Differential Equations and Their Developments, Kyoto University, November 13, 2019 (Invited Lecture). 

3. K. Ishibashi, Nonoscillation of Mathieu equations with two frequencies, University of Science & Technology Beijing School of Mathematics and Physics, Beijing China, November 13, 2018. (Special Lecture)

4. K. Ishibashi, A method of equivalent transformation of half-linear differential equations with damping, University of Science & Technology Beijing School of Mathematics and Physics, Beijing China, March 14, 2018.

5. K. Ishibashi, Nonoscillation of generalized Mathieu-type differential equations, Japan-China Student Workshop on Mathematics and Statistics in Matsue 2018, Shimane University, January 20, 2018.

6. K. Ishibashi, An equivalent transformation of half-linear differential equations with damping, China-Japan Joint Workshop on Ordinary Differential Equation, Dalian Minzu University, Dalian China, November 20, 2017.

7. K. Ishibashi, A nonoscillation theorem for generalized Mathieu-type differential equations, Japan-China Joint Workshop on Ordinary Differential Equations and Related Topics in Osaka 2017, Osaka Prefecture University, September 21, 2017.

8. K. Ishibashi, An equivalent transformation of half-linear differential equations,China-Japan Joint Workshop on Mathematics & Statistics, Northeast Normal University School of Mathematics and Statistics, Changchun China, September 12, 2017.

9. K. Ishibashi, Parameter region for oscillation and nonoscillation of generalized Mathieu differential equation, SAKURA Exchange Program in Science, Shimane University, August 22, 2017.

10. K. Ishibashi and J. Sugie, Three parameter space for nonoscillation of quasi-periodic Mathieu equations,China-Japan Joint Workshop on Mathematics & Statistics, Northeast Normal University School of Mathematics and Statistics, Changchun China, March 4, 2017.

11. K. Ishibashi and J. Sugie, Oscillation problems for Hill's equation with periodic damping, Japan-China Joint Workshop on Dynamical Systems in Okayama 2016, Okayama University of Science, December 2, 2016.

12. K. Ishibashi and J. Sugie, Nonoscillation criteria for Mathieu equations with coefficients of quasi-periodic, Japan-China Joint Workshop on Mathematical Sciences in Matsue 2016, Shimane University, November 30, 2016.

13. K. Ishibashi, Nonoscillation of quasi-periodic Mathieu equations with two frequencies, RIMS Workshop: Qualitative Theory of Ordinary Differential Equations and Related Areas, Kyoto University, November 16, 2016. (Invited Lecture) 

14. K. Ishibashi, Nonoscillation theorems for quasi-periodic Mathieu equations, China-Japan Joint Workshop on Mathematics & Statistics，Northeast Normal University School of Mathematics and Statistics, Changchun China, October 9, 2016. (Invited Lecture) 

15. K. Ishibashi and J. Sugie, Parametric excitation of generalized Mathieu equations, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing China, December 26, 2015.

16. K. Ishibashi and J. Sugie, Parametric excitation of generalized Mathieu equations, Academic Exchanges between Shimane University and Minnan Normal University, Minnan Normal University, Xiamen China, December 21, 2015.

17. K. Ishibashi and J. Sugie, Parameter region for oscillation of generalized Mathieu equations, 2015 International Workshop on Mathematical Sciences in Dalian, Dalian University School of Technology, Dalian China, October 30 to November 1, 2015.

18. L. She, K. Ishibashi and F. Wu, Nonoscillation criteria for linear difference equations, Japan-China Joint Workshop on Ordinary Differential Equations and Related Topics in Osaka 2015, Osaka Prefecture University, September 25, 2015.

19. K. Ishibashi and J. Sugie, Parameter region for oscillation of generalized Mathieu equations, Japan-China Joint Workshop on Ordinary Differential Equations and Related Topics in Matsue 2015, Shimane University, September 19-20, 2015.

20. K. Ishibashi, Oscillation theorem for half-linear differential equations with p(t)-Laplacian, Student Workshop on Ordinary Differential Equations and It's Application to Biological Models in NENU 2015, Northeast Normal University School of Mathematics and Statistics, Changchun China, September 12, 2015.

21. K. Ishibashi and J. Sugie, Geometrical conditions for oscillation of linear systems whose coefficients are periodic, Japan-China Joint Workshop on Ordinary Differential Equations and Related Topics in Osaka 2014, Osaka Prefecture University, October 15, 2014.

22. K. Ishibashi and J. Sugie, Geometrical conditions for oscillation of linear systems, The First China-Japan Seminar on Singularity Theory and It's Applications for Young Researchers, Northeast Normal University School of Mathematics and Statistics, Changchun China, September 4-9, 2014.