研究業績

研究業績

学術論文(査読付き)

  1. (with M. Shibata and T. Watanabe) Uniqueness of asymptotic limit of ground states for a class of quasilinear Schrödinger equation with $H^1$-critical growth in $\mathbb{R}^3$,
    preprint.
  2. (with M. Shibata and T. Watanabe) Asymptotic property of ground states for a class of quasilinear Schrödinger equations with $H^1$-critical growth,
    Calculus of Variations and Partial Differential Equations 58 (2019), No.3, Art.88, 29pp.
  3. (with M. Shibata and T. Watanabe) A note on the uniqueness and non-degeneracy of positive radial solutions for semilinear elliptic problems and its application,
    Acta Mathematica Scientia 38B (2018), No.4, 1121–1142.
  4. (with M. Shibata and T. Watanabe) Global uniqueness results for ground states for a class of quasilinear elliptic equations,
    Kodai Mathematical Journal 40 (2017), No.1, 117–142.
  5. (with T. Watanabe) Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with $H^1$-supercritical exponent,
    Journal of Differential Equations 260 (2016), No.3, 3086–3118.
  6. The existence of multiple positive solutions for a class of non-local elliptic problem in $\mathbb{R}^N$,
    Mathematische Nachrichten 288 (2015), No.5-6, 486–497.
  7. (with T. Watanabe) Uniqueness and non-degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity,
    Nonlinear Analysis: Theory, Methods & Applications 108 (2014), 275–290.
  8. (with M. Shibata and T. Watanabe) Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations in $\mathbb{R}^2$,
    Funkcialaj Ekvacioj 57 (2014), No.2, 297–317.
  9. (with M. Shibata and T. Watanabe) Blow up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with $H^1$-supercritical nonlinearities,
    Journal of Differential Equations 256 (2014), No.4, 1492–1514.
  10. (with M. Shibata and T. Watanabe) Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with general nonlinearities,
    Communications on Pure and Applied Analysis 13 (2014), No.1, 97–118.
  11. (with T. Watanabe) Asymptotic properties of ground states of quasilinear Schrödinger equations with $H^1$-subcritical exponent,
    Advanced Nonlinear Studies 12 (2012), No.2, 255–279.
  12. (with T. Watanabe) Uniqueness of the ground state solutions of quasilinear Schrödinger equations,
    Nonlinear Analysis: Theory, Methods & Applications 75 (2012), No.2, 819–833.
  13. (with T. Watanabe) $G$-invariant positive solutions for a quasilinear Schrödinger equation,
    Advances in Differential Equations 16 (2011), No.3-4, 289–324.
  14. Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems,
    Topological Methods in Nonlinear Analysis 25 (2005), No.2, 275–296.
  15. (with K. Tanaka and M. Terui) A remark on periodic solutions of singular Hamiltonian systems,
    NoDEA Nonlinear Differential Equations and Applications 12 (2005), No.3, 265–274.
  16. Periodic solutions of singular Hamiltonian systems with prescribed energy,
    Nonlinear Analysis: Theory, Methods & Applications 63 (2005), No.5-7, e1039–e1049. published electronically only.
  17. A positive solution of a nonhomogeneous elliptic equation in $\mathbb{R}^N$ with $G$-invariant nonlinearity,
    Communications in Partial Differential Equations 27 (2002), No.1-2, 1–22.
  18. (with K. Tanaka) Existence of positive solutions for a class of nonhomogeneous elliptic equations in $\mathbb{R}^N$,
    Nonlinear Analysis: Theory, Methods & Applications 48 (2002), No.5, 685–705.
  19. (with K. Tanaka) Multiple positive solutions for nonhomogeneous elliptic equations,
    Nonlinear Analysis: Theory, Methods & Applications 47 (2001), No.6, 3783–3793.
  20. (with K. Tanaka) Four positive solutions for the semilinear elliptic equation: $-\Delta u+u=a(x)u^p+f(x)$ in $\mathbb{R}^N$,
    Calculus of Variations and Partial Differential Equations 11 (2000), No.1, 63–95.
  21. (with K. Tanaka) Trudinger type inequalities in $\mathbb{R}^N$ and their best exponents,
    Proceedings of the American Mathematical Society 128 (2000), No.7, 2051–2057.

京都大学数理解析研究所講究録

  1. (with T. Wananabe) Uniqueness and non-degeneracy of positive radial solutions of quasilinear Schrödinger equations,
    No.1901 (2014), 99–115.
  2. (with T. Wananabe) Dual variational approach to a quasilinear Schrödinger equation arising in plasma physics,
    No.1740 (2011), 103–119.
  3. A positive solution of semilinear elliptic equation with $G$-invariant nonlinearity,
    No.1307 (2003), 157–174.
  4. Positive solutions for nonhomogeneous elliptic equations,
    No.1204 (2001), 50–57.
  5. Four positive solutions for a semilinear elliptic equation,
    No.1117 (1999), 1–8.
  6. (with K. Tanaka) A scale-invariant form of Trudinger-Moser inequality and its best exponent,
    No.1102 (1999), 148–153.

大学紀要,報告集,その他

  1. (with T. Wananabe) Uniqueness of the ground state solutions of quasilinear Schrödinger equations,
    Osaka City University Mathematical Preprint Series, 09-19 (2010).
  2. (with T. Wananabe) $G$-invariant positive solutions for a quasilinear Schrödinger equation,
    Osaka City University Mathematical Preprint Series, 09-17 (2009).
  3. $G$-不変な非線型項を持つ楕円型方程式の正値解について,
    第22回発展方程式若手セミナー報告集, (2000), 68–74.
  4. 変分法による非線型楕円型方程式の正値解の多重存在について,
    第21回発展方程式若手セミナー報告集, (1999), 69–74.
  5. 摂動項を伴う非斉次楕円型方程式の正値解の存在について,
    第20回発展方程式若手セミナー報告集, (1998), 82–87.

書評

  1. 変分問題入門 ー非線形楕円型方程式とハミルトン系ー(著者 田中和永)
    数学,64巻2号,(2012),217–221.

教科書

  1. 工学系の微分積分学 ー入門から応用までー(星賀彰,高野優,関根義浩,足達慎二 共著)
    学術図書出版社

修士論文,博士論文

  1. A Variational Study of Semilinear Elliptic Problems without the Palais-Smale Condition,
    Doctoral thesis, Waseda University, 2001.
    NDL-OPAC(国立国会図書館蔵書検索・申込システム)での検索結果
  2. 指数型の非線型項を持つ非斉次楕円型方程式の解の存在について,
    Master’s thesis, Waseda University, 1998.