KEIO RESEARCHERS INFORMATION SYSTEM

Career 【 Display / hide 】

Career 【 Display / hide 】

• 2010.04

  -

  2011.03

  Waseda University, Graduate School of Fundamental Science and Engineering, JSPS Research Fellowship for Young Scientists (DC2)

• 2011.04

  -

  2012.03

  Waseda University, Graduate School of Fundamental Science and Engineering, JSPS Research Fellowship for Young Scientists (PD)

• 2012.04

  -

  2014.05

  Tohoku University, Mathematical Insitutute, JSPS Research Fellowship for Young Scientists (PD)

• 2014.06

  -

  2015.02

  Tohoku University, Mathematical Institute, Assistant Professor

• 2015.03

  -

  2018.03

  Kanazawa University, Faculty of Mathematics and Physics, Institute of Science and Engineering, Associate Professor

display all >>

Academic Background 【 Display / hide 】

Academic Background 【 Display / hide 】

• 2002.04

  -

  2006.03

  Waseda University, School of Science and Engineering, Department of Mathematical Sciences

  University, Graduated, Other

• 2006.04

  -

  2008.03

  Waseda University, Graduate School of Science and Engineering, Department of Mathematical Sciences

  Graduate School, Completed, Master's course

• 2008.04

  -

  2011.03

  Waseda University, Graduate School of Fundamental Science and Engineering,  Department of Pure and Applied Mathematics

  Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide 】

Academic Degrees 【 Display / hide 】

• Doctor(Science), Waseda University, Coursework, 2011.03

Research Areas 【 Display / hide 】

Research Areas 【 Display / hide 】

• Natural Science / Mathematical analysis ( Variational methods, Critical point theory, Nonlinear elliptic differential equations, Geometric analysis.)

Research Keywords 【 Display / hide 】

Research Keywords 【 Display / hide 】

• Variational methods, Critical point theory, Nonlinear elliptic differential equations, Geometric analysis.

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• Compactness via monotonicity in nonsmooth critical point theory, with application to Born–Infeld type equations

  Byeon J., Ikoma N., Malchiodi A., Mari L.

  Journal of Functional Analysis 290 ( 11 )  2026.06

  ISSN  00221236

  　View Summary

  In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the Palais–Smale condition. We apply our abstract results to get entire solutions with finite energy to Born–Infeld type autonomous equations. More precisely, under almost optimal conditions on the nonlinearity, we construct a positive solution and infinitely many solutions both in the classes of radially symmetric functions and nonradiallly symmetric ones.

  • Access to Document (DOI)

• Existence and order of the self–binding transition in non–local non–linear Schrödinger equations

  Ikoma N., Myśliwy K.

  Calculus of Variations and Partial Differential Equations 65 ( 4 )  2026.04

  ISSN  09442669

  　View Summary

  We consider a class of non–linear and non–local functionals giving rise to the Choquard equation with a suitably regular interaction potential, modelling, i.a., gases with impurities and axion stars. We study how existence of minimizers depends on the coupling constant, and find that there is a critical interaction strength needed for the minimizers to exist, both in dimensions two and three. In d=3, a minimizer exists also at the critical coupling but none do in d=2 under suitable assumptions on the potential. We also establish that in d=3 there exist other critical points beyond the global minimizer.

  • Access to Document (DOI)

• NORMALIZED GROUND STATES FOR NLS EQUATIONS WITH MASS CRITICAL NONLINEARITIES

  Cingolani S., Gallo M., Ikoma N., Tanaka K.

  Discrete and Continuous Dynamical Systems Series A 53   210 - 240 2026

  ISSN  10780947

  　View Summary

  We study normalized solutions (µ, u) ∈ R × H¹(R^N) to nonlinear Schrödinger equations −∆u + µu = g(u) in R^N<inf>2</inf>^{1 Z}<inf>RN</inf> u²dx = m, where N ≥ 2 and the mass m > 0 is given. Here, g has an L²-critical growth, both at the origin and at infinity, that is, g(s) ∼ |s|^p−¹s as s ∼ 0 and s ∼ ∞, where p = 1 + <inf>N</inf>⁴ . We continue the analysis started in [11], where we found two (possibly distinct) minimax values b ≤ 0 ≤ b of the Lagrangian functional. In this paper, we furnish explicit examples of g satisfying b < 0 < b, b = 0 < b, and b < 0 = b; notice that b = 0 = b in the power case g(t) = |t|^p−¹t. Moreover, we deal with the existence and non-existence of a solution with minimal energy. Finally, we discuss the assumptions required on g to obtain the existence of a positive solution for perturbations of g.

  • Access to Document (DOI)

• Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model

  Jaeyoung Byeon, Norihisa Ikoma, Andrea Malchiodi, Luciano Mari

  Annals of PDE (Springer Science and Business Media LLC)  10 ( 1 )  2024.06

  Accepted,  ISSN  25245317

  　View Summary

  Given a measure ρ on a domain Ω ⊂ Rm , we study spacelike graphs over Ω in Minkowski space with Lorentzian mean curvature ρ and Dirichlet boundary condition on ∂Ω , which solve [Figure not available: see fulltext.] The graph function also represents the electric potential generated by a charge ρ in electrostatic Born-Infeld’s theory. Even though there exists a unique minimizer uρ of the associated action Iρ(ψ)≐∫Ω(1-1-|Dψ|2)dx-⟨ρ,ψ⟩ among functions ψ satisfying | Dψ| ≤ 1 , by the lack of smoothness of the Lagrangian density for | Dψ| = 1 one cannot guarantee that uρ satisfies the Euler-Lagrange equation (BI). A chief difficulty comes from the possible presence of light segments in the graph of uρ . In this paper, we investigate the existence of a solution for general ρ . In particular, we give sufficient conditions to guarantee that uρ solves (BI) and enjoys log -improved energy and Wloc2,2 estimate. Furthermore, we construct examples which suggest a sharp threshold for the regularity of ρ to ensure the solvability of (BI).

  • Access to Document (DOI)

• The existence and multiplicity of L^2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

  Norihisa Ikoma, Mizuki Yamanobe

  Advanced Nonlinear Studies (Walter de Gruyter GmbH)  24 ( 2 ) 477 - 509 2024.04

  Accepted,  ISSN  1536-1365

  　View Summary

  Abstract
  
  The existence of L ²–normalized solutions is studied for the equation − Δ u + μ u = f ( x , u )     in R N , ∫ R N u 2 d x = m . $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R } }^{N},\quad {\int }_{ { \mathbf{R } }^{N } }{u}^{2} \mathrm{d}x=m.$ Here m &gt; 0 and f(x, s) are given, f(x, s) has the L ²-subcritical growth and (μ, u) ∈ R × H ¹(R ^N) are unknown. In this paper, we employ the argument in Hirata and Tanaka (“Nonlinear scalar field equations with L ² constraint: mountain pass and symmetric mountain pass approaches,” Adv. Nonlinear Stud., vol. 19, no. 2, pp. 263–290, 2019) and find critical points of the Lagrangian function. To obtain critical points of the Lagrangian function, we use the Palais–Smale–Cerami condition instead of Condition (PSP) in Hirata and Tanaka (“Nonlinear scalar field equations with L ² constraint: mountain pass and symmetric mountain pass approaches,” Adv. Nonlinear Stud., vol. 19, no. 2, pp. 263–290, 2019). We also prove the multiplicity result under the radial symmetry.

  • Access to Document (DOI)

display all >>

Papers, etc., Registered in KOARA 【 Display / hide 】

Papers, etc., Registered in KOARA 【 Display / hide 】

• Study of the strucure of solutions to nonlinear elliptic equations with various effects

  Ikoma, Norihisa

  科学研究費補助金研究成果報告書 2023

• Nonlinear elliptic partial differential equations having variation structure

  Ikoma, Norihisa

  科学研究費補助金研究成果報告書 2018

Reviews, Commentaries, etc. 【 Display / hide 】

Reviews, Commentaries, etc. 【 Display / hide 】

• Kirchhoff型方程式に対する特異摂動問題 (パターン形成と界面ダイナミクスの数理)

  生駒 典久

  数理解析研究所講究録 (京都大学数理解析研究所)  1979   89 - 106 2015.12

  ISSN  1880-2818

  • CiNii Research

• Some properties of eigenvalues for fully nonlinear operators (Qualitative theory of ordinary differential equations in real domains and its applications)

  Ikoma Norihisa

  RIMS Kokyuroku (Kyoto University)  1959   128 - 141 2015.07

  ISSN  1880-2818

  • CiNii Research

• Existence of eigenvalues and eigenfunctions for radially symmetric fully nonlinear elliptic operators (Regularity and Singularity for Geometric Partial Differential Equations and Conservation Laws)

  Ikoma Norihisa

  RIMS Kokyuroku (Kyoto University)  1845   84 - 106 2013.07

  ISSN  1880-2818

  • CiNii Research

• A singular perturbation problem for coupled nonlinear Schrodinger equations (Variational Problems and Related Topics)

  Ikoma Norihisa

  RIMS Kokyuroku (Kyoto University)  1671   1 - 19 2009.12

  ISSN  1880-2818

  • CiNii Research

Presentations 【 Display / hide 】

Presentations 【 Display / hide 】

• Ground state solutions to Born-Infeld type equations

  Norihisa Ikoma

  [International presentation]  Semilinear elliptic equations and related topics, 

  2026.01

  , 

  Oral presentation (invited, special)

• Existence of L^2-normalized solutions to nonlocal and nonlinear Schroedinger equation

  Norihisa Ikoma

  [International presentation]  Recent advances and challenges in partial differential equations, 

  2025.09

  , 

  Oral presentation (invited, special)

• Existence of L^2-normalized solutions to equations with nonlocal and nonlinear potentials

  Norihisa Ikoma

  [International presentation]  UK-Japan Workshop on Nonlinear PDEs:Singularities and asymptotic patterns inFluids, Chemotaxis and Geometric PDEs, 

  2025.06

  -

  2025.07

  , 

  Oral presentation (invited, special)

• Monotonicity trick in nonsmooth critical point theory and its application

  Norihisa Ikoma

  [International presentation]  The 14th AIMS Conference, Special Session 72: Nonlinear elliptic PDEs, 

  2024.12

  , 

  Oral presentation (invited, special)

• The existence of L^2-normalized solutions in the L^2-critical setting

  Norihisa Ikoma

  [International presentation]  The 14th AIMS Conference, Sepcial Session 2: Recent advances in nonlinear Schroedinger systems, 

  2024.12

  , 

  Oral presentation (invited, special)

display all >>

Research Projects of Competitive Funds, etc. 【 Display / hide 】

Research Projects of Competitive Funds, etc. 【 Display / hide 】

• 特異性や制約条件を持つ非線形楕円型方程式の解構造の研究

  2024.04

  -

  2028.03

  日本学術振興会, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  　View Summary

  本研究課題では，変分構造を持つ非線形楕円型方程式に対し，解の存在や解の性質を明らかにすることを目標にしている．本課題で扱う非線形楕円型方程式は物理学や幾何学において現れ，解の存在やその性質を調べることは重要であるが，解の陽的な表示を得ることは非常に難しく，ほとんど不可能であるように思える．そのため解の陽的な表示を使わずに特定の性質を持った解の存在を示したり，解があったとすると特定の性質を必ず持つ，ということを明らかにしたい．

• Study of solution structures of elliptic equations: supercritical, critical and subcritocal cases

  2019.04

  -

  2024.03

  日本学術振興会, Grants-in-Aid for Scientific Research, Miyamoto Yasuhito, Grant-in-Aid for Scientific Research (B), No Setting

  　View Summary

  Solution structures, which are bifurcation diagrams, of supercritical elliptic Dirichlet problem are studied. It is known that standard variational approaches, which are used to study subcritical problems, are not applicable to supercritical problems. A large part of a solution structure was not known. In this study we consider positive solutions of elliptic Dirichlet problem when the domain is a ball. We show that a positive radial singular solution of the supercritical elliptic equation plays a crucial role in the study of bifurcation diagrams. We prove the existence and uniqueness of a positive radial singular solution and obtain an asymptotic expansion of the singular solution near the singular point. We apply our theory to several interesting elliptic equations and classify the bifurcation diagrams.

• Study of the strucure of solutions to nonlinear elliptic equations with various effects

  2019.04

  -

  2023.03

  MEXT,JSPS, Grant-in-Aid for Scientific Research, Ikoma Norihisa, Grant-in-Aid for Scientific Research (C), Principal investigator

  　View Summary

  The aim of this research project was to investigate the structure of nontrivial solutions to elliptic equations involving singularities, nonlocalities and so on. During the period, the following results were obtained. For the Born-Infeld equation(this equation has a singularity), the regularity of minimizer as well as the relation between minimizers and weak solutions were studied. For the equation with the fractional Laplacian and the Hardy-Henon type nonlinearity (the equation has a nonlocality), the existence and nonexistence of stables solutions was proved. The layer property of the family of stable solutions were also shown. In addition to these two equations, the existence of nontrivial solutions and their properties were obtained for the equation with sublinear nonlinearities, a class of equations involving the 1 dimensional Pucci operators, the equation with large parameters and the equation with a constraint on the L^2 norm of solutions.

• Analysis of large time behavior of solution to nonlinear partial differential equations with dispersion

  2017.04

  -

  2021.03

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Segata Jun-ichi, Grant-in-Aid for Scientific Research (B), No Setting

  　View Summary

  Nonlinear dispersive partial differential equation is one of important class in the partial differential equations. Due to a complex interaction between dispersive and nonlinear effects in the equation, there is a wide variety of asymptotic behavior of solution, and it is difficult to study long time behavior of solution. In this research, we tried to gain a new insight on long time behavior of solution to nonlinear dispersive equation by analyzing concrete models via harmonic analysis and variational methods.

• Nonlinear elliptic partial differential equations having variation structure

  2016.04

  -

  2019.03

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Ikoma Norihisa, Grant-in-Aid for Young Scientists (B), No Setting

  　View Summary

  In this project, the existence of solutions and their properties were studied for nonlinear elliptic partial differential equations. In particular, we treated equations which have variational structure (for instance, equations with fractional operators of elliptic operators). We proved the existence of solutions satisfying some properties and showed the existence of multiple solutions. We also studied a variant of the Trudinger-Moser inequality and found conditions when the inequality is satisfied as an equality. This inequality is related to a certain nonlinear elliptic partial differential equation.

Other 【 Display / hide 】

Other 【 Display / hide 】

• 　View Details

  バリ工科大学(Politecnico di Bari)機械数学経営学科(Department of Mechanics, Mathematics and Management)による Visiting Professor の公募に応募，当選し，2026年3月2日から2026年5月2日までバリ工科大学に滞在し，ホスト教員である Alessio Pomponio 氏と共同研究を行い，Ph.D学生向けのミニ講義を行った．

Courses Taught 【 Display / hide 】

Courses Taught 【 Display / hide 】

• DOCTORAL RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY C

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY F

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY B

  2026

• GRADUATE RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES 2

  2026

display all >>

Courses Previously Taught 【 Display / hide 】

Courses Previously Taught 【 Display / hide 】

• 数理科学特論2，数理科学特別講義 II

  九州大学

  2025.11

  , 

  Other, Other, Lecture, Within own ｆaculty

• 数学特論Ⅶ

  埼玉大学

  2025.08

  , 

  Other, Other, Lecture, Within own ｆaculty

• 数学特別講義Ｃ

  東北大学

  2025.06

  , 

  Other, Other, Lecture, Within own ｆaculty

• 数理科学特論Ａ

  早稲田大学

  2022.11

  , 

  Other, Lecture, Within own ｆaculty

• 数学特別講義XX

  大阪大学

  2022.06

  -

  2022.07

  , 

  Other, Other, Lecture, Within own ｆaculty

display all >>

Committee Experiences 【 Display / hide 】

Committee Experiences 【 Display / hide 】

• 2021.07

  -

  2023.06

  雑誌数学編集委員, 日本数学会

• 2020.04

  -

  2022.03

  函数方程式論分科会　情報委員会　運営委員, 日本数学会関数方程式函数方程式論分科会