Office
E6-1, Rm. 4401, 291 Daehak-ro, Yuseong-gu, Daejeon, Republic of Korea, 34141

Contact
byeon@kaist.ac.kr

Education

  • 1988.02
    BS, Mathematics, Seoul National University
  • 1990.02
    MS, Mathematics, Seoul National University (academic advisor : Jongsik Kim)
  • 1991.01
    The Third Military Academy(Military Service; Second Lieutenant)
  • 1996.09
    PhD, Graduate School of Mathematical Sciences, University of Tokyo (academic advisor : Hiroshi Matano)


Professional Career:

  • 1996.10 - 1997.02
    Postdoctoral Research Fellow of Global Analysis Research Center in Seoul National University
  • 1997.03 - 1997.06
    Postdoctoral Research Fellow in KAIST through support from KOSEF
  • 1997.07 - 1998.06
    Research Fellow in Korea Institute for Advanced Study
  • 1998.07 – 2013.01
    Assistant, Associate and Full Professor, Department of Mathematics, Pohang University of Science and Technology(POSTECH)
  • 2013.02 - present
    Professor in Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST)

Research fields
· Partial Differential Equations
· Calculus of Variations
· Nonlinear Analysis
· Geometric Analysis


Topics of research works

  1. Symmetry and Symmetry breaking for elliptic PDEs
  2. Elliptic problems on singularly perturbed domains
  3. Standing waves with a critical frequency
  4. Singularly perturbed nonlinear elliptic problems on manifolds
  5. Construction of solutions for singularly perturbed nonlinear elliptic problems under Berestycki-Lions condition
  6. Asymptotic behaviour of least energy solution for the Henon equation
  7. Standing waves of the Chern-Simons-Schrödinger equation
  8. Phase transition solutions for an Allen-Cahn model and further development of a work of Moser on a PDE version of Aubry-Mather theory
  9. Elliptic systems with large interaction forces
  10. Hardy type inequalities
  11. Rigidity of the scalar curvature

Awards and Honors

  • 2021 : Member of the Korean Academy of Science and Technology
  • 2018 : International Exchanges Award by The Royal Society
  • KAIST Top Ten Research Achievements in 2017 (KAIST)
  • Scientist of the month, July 2016(Ministry of Science, ICT and Future Planning)
  • KAIST Top Ten Research Achievements in 2014 (KAIST)
  • KAIST Chair Professor, 2014.03—2017.02 (KAIST)
  • Kwun Kyungwhan Chair Professor, 2007.08—20010.07(POSTECH)
  • The 10th anniversary best alumni of KIAS, 2006 (KIAS)
  • The 8-th Young Scientist Award, 2004 (President of Republic of Korea)
  • JSPS fellowship through School of Mathematical Sciences, University of Tokyo (1993.10-1996.09)

Editorial Services

  • Editor for Communications in Pure and Applied Analysis since 2011
  • Managing Editor of Journal of the Korean Mathematical Society, 2019-2023


Other services

  • Committee Chair (2018.01-2020.12) of Analysis Section in the Korean Mathematical Society,
  • Review Board of Analysis section for NRF(2018.11.01-2021.10.31)
  • Department Head of Department of Mathematical Sciences, KAIST(2021-present)

Graduate Students
    Yeonho Kim,  Juneyoung Seo,  Eunchan Chon,  Woojin Ko.
 

Alumni(PhD)

  • Junsang Park(2007, POSTECH) now in a company
  • Ohsang Kwon(2010, POSETECH) now in Chungbuk National University
  • Jinmyeong Seok(2012.02, POSTECH) now in Kyunggi University
  • Youngae Lee(2012.08, POSTECH) now in Kyungbuk National University
  • Seunghyeok Kim(2013.02, POSTECH) now in Hanyang University
  • Wonjeong Jeong(2013.08, POSTECH) now in a company
  • Sang-hyuck Moon(2019.02, KAIST) now in NCTS, Taiwan
  • Sangdon Jin(2020.02, KAIST) now in SAARC, KAIST

Preprints

  1. ...

Journal articles

  1. Positive vector solutions for nonlinear Schrödinger systems with strong interspecies attractive forces, J. Math. Pures Appl. (9) 143 (2020), 73–115 (with Kwon, Ohsang and Seok, Jinmyoung). MR4163124
  2. Least energy solution for a scalar field equation with a singular nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A (2020), Advance online publication (with Choi, Sun-Ho and Kim, Yeonho and Moon, Sang-hyuck). doi:10.1017/prm.2020.4
  3. Hardy's inequality in a limiting case on general bounded domains, Commun. Contemp. Math. 21 (2019), no. 8, 1850070, 24 pp (with Takahashi, Futoshi). MR4020754
  4. Formation of radial patterns via mixed attractive and repulsive interactions for Schrödinger systems, SIAM J. Math. Anal. 51 (2019), no. 2, 1514–1542. (with Lee, Youngae and Wang, Zhi-Qiang). MR3945240
  5. Spike layer solutions for a singularly perturbed Neumann problem: variational construction without a nondegeneracy, Commun. Pure Appl. Anal. 18 (2019), no. 4, 1921–1965. (with Moon, Sang-hyuck). MR3927426
  6. The Hénon equation with a critical exponent under the Neumann boundary condition, Discrete Contin. Dyn. Syst. 38 (2018), no. 9, 4353–4390. (with Jin, Sangdon). MR3824706
  7. On the Hénon equation with a Neumann boundary condition: asymptotic profile of ground states, J. Funct. Anal. 274 (2018), no. 12, 3325–3376 (with Wang, Zhi-Qiang). MR3787594
  8. Nonlinear scalar field equations involving the fractional Laplacian, Nonlinearity 30 (2017), no. 4, 1659–1681 (with Kwon, Ohsang and Seok, Jinmyoung). MR3636314
  9. Pattern formation via mixed interactions for coupled Schrödinger equations under Neumann boundary condition, J. Fixed Point Theory Appl. 19 (2017), no. 1, 559–583 (with Sato, Yohei and Wang, Zhi-Qiang). MR3625084
  10. A double well potential system, Anal. PDE J. Fixed Point Theory Appl. 9 (2016), no. 7, 1737–1772 (with Montecchiari, Piero and Rabinowitz, Paul H.). MR3570237
  11. Pattern formation via mixed attractive and repulsive interactions for nonlinear Schrödinger systems, J. Math. Pures Appl. (9) 106 (2016), no. 3, 477–511 (with Sato, Yohei and Wang, Zhi-Qiang). MR3520445
  12. On standing waves with a vortex point of order N for the nonlinear Chern-Simons-Schrödinger equations, J. Differential Equations 261 (2016), no. 2, 1285–1316 (with Huh, Hyungjin and Seok, Jinmyoung). MR3494398
  13. Unbounded solutions for a periodic phase transition model, J. Differential Equations 260 (2016), no. 2, 1126–1153 (with Rabinowitz, Paul H.). MR3419723
  14. Semi-classical standing waves for nonlinear Schrödinger systems, Calc. Var. Partial Differential Equations 54 (2015), no. 2, 2287–2340. MR3396454
  15. Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations, Commun. Pure Appl. Anal. 14 (2015), no. 3, 825–842 (with Kwon, Ohsang and Oshita, Yoshihito). MR3320153
  16. Solutions of higher topological type for an Allen-Cahn model equation, J. Fixed Point Theory Appl. 15 (2014), no. 2, 379–404 (with Rabinowitz, Paul H.). MR3298005
  17. Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains, Calc. Var. Partial Differential Equations 50 (2014), no. 1-2, 365–397 (with Tanaka, Kazunaga). MR3194687
  18. Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations, Mem. Amer. Math. Soc. 229 (2014), no. 1076, viii+89 pp. ISBN: 978-0-8218-9163-6 (with Tanaka, Kazunaga). MR3186497
  19. Asymptotic behavior of minima and mountain pass solutions for a class of Allen-Cahn models, Commun. Inf. Syst. 13 (2013), no. 1, 79–95 (with Rabinowitz, Paul H.). MR3216987
  20. Existence of clustering high dimensional bump solutions of superlinear elliptic problems on expanding annuli, J. Funct. Anal. 265 (2013), no. 9, 1955–1980 (with Kim, Seunghyeok and Pistoia, Angela). MR3084494
  21. Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1859–1899 (with Tanaka, Kazunaga). MR3082247
  22. Singularly perturbed nonlinear Dirichlet problems involving critical growth, Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 65–85 (with Zhang, Jianjun and Zou, Wenming). MR3044132
  23. On a phase transition model, Calc. Var. Partial Differential Equations 47 (2013), no. 1-2, 1–23 (with Rabinowitz, Paul H.). MR3044129
  24. Variational approach to bifurcation from infinity for nonlinear elliptic problems, Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 2, 269–301 (with Lee, Youngae). MR3039812
  25. Standing waves of nonlinear Schrödinger equations with optimal conditions for potential and nonlinearity, Commun. Pure Appl. Anal. 12 (2013), no. 2, 831–850 (with Bae, Soohyun). MR2982793
  26. Nonlinear elliptic equations in strip-like domains, Adv. Nonlinear Stud. 12 (2012), no. 4, 749–765 (with Tanaka, Kazunaga). MR3012860
  27. Standing waves of nonlinear Schrödinger equations with the gauge field, J. Funct. Anal. 263 (2012), no. 6, 1575–1608 (with Huh, Hyungjin and Seok, Jinmyoung). MR2948224
  28. Singularly perturbed nonlinear Neumann problems under the conditions of Berestycki and Lions, J. Differential Equations 252 (2012), no. 6, 3848–3872. MR2875604
  29. On the location of a peak point of a least energy solution for Hénon equation, Discrete Contin. Dyn. Syst. 30 (2011), no. 4, 1055–1081 (with Cho, Sungwon and Park, Junsang). MR2812953
  30. Multi-bump standing waves with critical frequency for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 4, 1121–1152 (with Oshita, Yoshihito). MR2659160
  31. Singularly perturbed nonlinear Dirichlet problems with a general nonlinearity, Trans. Amer. Math. Soc. 362 (2010), no. 4, 1981–2001. MR2574884
  32. Symmetry and monotonicity of least energy solutions, Calc. Var. Partial Differential Equations 36 (2009), no. 4, 481–492 (with Jeanjean, Louisand Mariş, Mihai ). MR2558325
  33. Standing waves for nonlinear Schrödinger equations with singular potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, 943–958 (with Wang, Zhi-Qiang). MR2526410
  34. Uniqueness of standing waves for nonlinear Schrödinger equations, Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), no. 5, 975–987 (with Oshita, Yoshihito). MR2477447
  35. Standing waves for nonlinear Schrödinger equations with a general nonlinearity: one and two dimensional cases, Comm. Partial Differential Equations 33 (2008), no. 4-6, 1113–1136 (with Jeanjean, Louis and Tanaka, Kazunaga). MR2424391
  36. Singularly perturbed nonlinear Neumann problems with a general nonlinearity, J. Differential Equations 244 (2008), no. 10, 2473–2497. MR2414402
  37. Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity, Discrete Contin. Dyn. Syst. 19 (2007), no. 2, 255–269 (with Jeanjean, Louis). MR2335747
  38. Standing waves for nonlinear Schrödinger equations with a general nonlinearity, Arch. Ration. Mech. Anal. 185 (2007), no. 2, 185–200 (with Jeanjean, Louis). MR2317788
    Erratum: Arch. Ration. Mech. Anal. 190 (2008), no. 3, 549–551. MR2448327
  39. On the Hénon equation: asymptotic profile of ground states. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 6, 803–828 (with Wang, Zhi-Qiang). MR2271694
  40. Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potentials, J. Eur. Math. Soc. (JEMS) 8 (2006), no. 2, 217–228 (with Wang, Zhi-Qiang). MR2239273
  41. Singularly perturbed nonlinear elliptic problems on manifolds, Calc. Var. Partial Differential Equations 24 (2005), no. 4, 459–477 (with Park, Junsang). MR2180862
  42. Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems, J. Differential Equations 217 (2005), no. 2, 257–281. MR2168823
  43. On the Hénon equation: asymptotic profile of ground states. II, J. Differential Equations 216 (2005), no. 1, 78–108 (with Wang, Zhi-Qiang). MR2158918
  44. Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations, Comm. Partial Differential Equations 29 (2004), no. 11-12, 1877–1904 (with Oshita, Yoshihito). MR2106071
  45. Standing waves with a critical frequency for nonlinear Schrödinger equations. II, Calc. Var. Partial Differential Equations 18 (2003), no. 2, 207–219 (with Wang, Zhi-Qiang). MR2010966
  46. Standing wave solutions with a critical frequency for nonlinear Schrödinger equations. Topological methods, variational methods and their applications, (Taiyuan, 2002), 45–52, World Sci. Publ., River Edge, NJ, 2003 (with Wang, Zhi-Qiang). MR2010640
  47. Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165 (2002), no. 4, 295–316 (with Wang, Zhi-Qiang). MR1939214
  48. Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems. III, Asymptot. Anal. 30 (2002), no. 3-4, 249–272. MR1932038
  49. Symmetry breaking of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities, Commun. Contemp. Math. 4 (2002), no. 3, 457–465 (with Wang, Zhi-Qiang). MR1918754
  50. Standing waves for nonlinear Schrödinger equations with a radial potential, Nonlinear Anal. 50 (2002), no. 8, Ser. A: Theory Methods, 1135–1151. MR1914233
  51. Singularly perturbed nonlinear Neumann problems on symmetric domains, Comm. Partial Differential Equations 26 (2001), no. 9-10, 1607–1631. MR1865939
  52. Nonlinear elliptic problems on singularly perturbed domains, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 5, 1023–1037. MR1862441
  53. Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems. II, J. Differential Equations 173 (2001), no. 2, 321–355. MR1834118
  54. Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Equations 163 (2000), no. 2, 429–474. MR1758705
  55. Nonlinear elliptic problems on rotationally symmetric domains. Variational problems and related topics, (Japanese) (Kyoto, 1997) Sūrikaisekikenkyūsho Kōkyūroku No. 1025 (1998), 5–19. MR1644791
  56. Existence of large positive solutions of some nonlinear elliptic equations on singularly perturbed domains, Comm. Partial Differential Equations 22 (1997), no. 9-10, 1731–1769. MR1469588
  57. Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli, J. Differential Equations 136 (1997), no. 1, 136–165. MR1443327

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SAARC

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Stochastic Analysis and Application Research Center

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Tel. +82-42-350-8111/8117

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Journal of the Korean Mathematical Society

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eISSN 2234-3008

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Communications on Pure and Applied Analysis

ISSN: 1534-0392

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