{
  "id": "1605.04178",
  "version": "v1",
  "published": "2016-05-13T13:44:04.000Z",
  "updated": "2016-05-13T13:44:04.000Z",
  "title": "Nonlinear elliptic equations and systems with linear part at resonance",
  "authors": [
    "Philip Korman"
  ],
  "comment": "17 pages",
  "journal": "Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 67, pp. 1--17",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples were ever given. We show that seemingly different classical result by Lazer and Leach [11], on forced harmonic oscillators at resonance, provides an example for this theorem. The article by Williams [14] also contained a shorter proof. We use a similar approach to study resonance for $2 \\times 2$ systems. We derive conditions for existence of solutions, which turned out to depend on the spectral properties of the linear part.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-13T13:44:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35J47"
    ],
    "keywords": [
      "nonlinear elliptic equations",
      "linear part",
      "study resonance",
      "similar approach",
      "shorter proof"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}