{
  "id": "1402.3784",
  "version": "v2",
  "published": "2014-02-16T11:11:58.000Z",
  "updated": "2016-04-13T16:26:34.000Z",
  "title": "New blow-up phenomena for SU(n+1) Toda system",
  "authors": [
    "Monica Musso",
    "Angela Pistoia",
    "Juncheng Wei"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1210.5719",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the $SU(n+1)$ Toda system $$(S_\\lambda) \\quad \\left\\{ \\begin{aligned} & \\Delta u_1 + 2\\lambda e^{u_1} - \\lambda e^{u_2}- \\dots - \\lambda e^{u_k} = 0\\quad \\hbox{in}\\ \\Omega,\\\\ & \\Delta u_2 - \\lambda e^{u_1} + 2\\lambda e^{u_2} - \\dots - \\lambda e^{u_k}=0\\quad \\hbox{in}\\ \\Omega,\\\\ &\\vdots \\hskip3truecm \\ddots \\hskip2truecm \\vdots\\\\ & \\Delta u_k -\\lambda e^{u_1}-\\lambda e^{u_2}- \\dots+2\\lambda e^{u_k}=0\\quad \\hbox{in}\\ \\Omega, &u_1 = u_2 = \\dots = u_k =0 \\quad \\hbox{on}\\ \\partial\\Omega.\\\\ \\end{aligned}\\right. $$ If $0\\in\\Omega$ and $\\Omega$ is symmetric with respect to the origin, we construct a family of solutions $({u_1}_\\lambda,\\dots,{u_k}_\\lambda)$ to $(S_\\lambda )$ such that the $i-$th component ${u_i}_\\lambda$ blows-up at the origin with a mass $2^{i+1}\\pi $ as $\\lambda$ goes to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-16T11:11:58.000Z",
      "abstract": "We consider the $SU(n+1)$ Toda system $$\\(S_\\lambda\\)\\quad \\left\\{\\begin{aligned} & \\Delta u_1+2\\lambda e^{u_1}-\\lambda e^{u_2}- \\dots-\\lambda e^{u_k}=0\\quad \\hbox{in}\\ \\Omega,\\\\ & \\Delta u_2-\\lambda e^{u_1}+2\\lambda e^{u_2}- \\dots-\\lambda e^{u_k}=0\\quad \\hbox{in}\\ \\Omega,\\\\ &\\vdots \\hskip3truecm \\ddots \\hskip2truecm \\vdots\\\\ & \\Delta u_k -\\lambda e^{u_1}-\\lambda e^{u_2}- \\dots+2\\lambda e^{u_k}=0\\quad \\hbox{in}\\ \\Omega, &u_1=u_2=\\dots=u_k=0\\quad \\hbox{on}\\ \\partial\\Omega.\\\\ \\end{aligned}\\right. $$ If $0\\in\\Omega$ and $\\Omega$ is symmetric with respect to the origin, we construct a family of solutions $({u_1}_\\la,\\dots,{u_k}_\\la)$ to $(S_\\la )$ such that the $i-$th component ${u_i}_\\la$ blows-up at the origin with a mass $2^{i+1}\\pi $ as $\\la$ goes to zero.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-13T16:26:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toda system",
      "blow-up phenomena",
      "th component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1281736,
      "adsabs": "2014arXiv1402.3784M"
    }
  }
}