Areas of Expertise

Mathematical analysis focusing on solvability of singular nonlinear partial differential equations.

Teaching Interests

Dr. Bacani has taught a variety of mathematics courses—including College Algebra, Trigonometry, Pre-Calculus, Calculus, Linear Algebra, Abstract Algebra, Real Analysis, Differential Equations, and Topology—to a wide range of undergraduate students.


Dennis Bacani’s research has been focused in the field of partial differential equations. He has investigated convergence of formal solutions, existence and uniqueness of solutions, and lifespan of solutions to nonlinear partial differential equations.

Representative Publications

  • Bacani, D.B. & Lope, J. E. C. (2018). Solvability of a class of higher order singular nonlinear partial differential equations. Southeast Asian Bulletin of Mathematics, 42, 809-824.
  • Bacani, D. B., Lope, J. E. C. & Tahara, H. (2018). On the unique solvability of nonlinear Fuchsian partial differential equations. Tokyo Journal of Mathematics, 41(1), 225-259.
  • Tolentino, M. A. C., Bacani, D.B., & Tahara, H. (2016). On the lifespan of solutions to nonlinear Cauchy problems with small analytic data. Journal of Differential Equations, 260(1), 897-922.
  • Bacani, D. B. & Tahara, H. (2014). Unique solvability of totally characteristic type singular nonlinear partial differential equations. Journal of the Mathematical Society of Japan 66(3), 1017-1042.
  • Bacani, D. B. & Tahara, H. (2013). On existence and uniqueness theorems for singular nonlinear partial differential equations. RIMS Kokyuroku Bessatsu, B40, 69 – 79.
  • Bacani, D. B. & Tahara, H. (2012). Existence and uniqueness theorem for a class of singular nonlinear partial differential equations. Publications of the Research Institute for Mathematical Sciences Kyoto University, 48, 899 – 917.
  • He also has a Youtube channel, K.O. Math ( ), where he shares Math tutorial videos.


Ph.D., Mathematics, Sophia University, Japan

M.S., Mathematics, University of the Philippines

B.S., Mathematics, University of the Philippines

Previous Appointments

Research Fellow and Assistant Professor at Sophia University, Japan (2013-2017)

Instructor and Assistant Professor at University of the Philippines (2001-2009)

Instructor at AMA Computer College, Philippines (2000-2001)