{
  "id": "1101.1827",
  "version": "v1",
  "published": "2011-01-10T14:28:12.000Z",
  "updated": "2011-01-10T14:28:12.000Z",
  "title": "Non-standard eigenvalue problems for perturbed $p$-Laplacians",
  "authors": [
    "Faruk Güngör",
    "Mahir Hasanov"
  ],
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "This paper is devoted to multi-parameter eigenvalue problems for perturbed $p$-Laplacians, modelling travelling waves for a class of non-linear evolution PDE. Dispersion relations between the eigen-para-meters, the existence of eigenvectors and positive eigenvectors, variational principles for eigenvalues of perturbed $p$-Laplacians and constructing analytical solutions are the main subject of this paper. Besides the $p$-Laplacian-like eigenvalue problems we also deal with new and non-standard eigenvalue problems, which can not be solved by the methods used in nonlinear eigenvalue problems for $p$-Laplacians and similar operators. We do both: extend and use classical variational and analytical techniques to solve standard eigenvalue problems and suggest new variational and analytical methods to solve the non-standard eigenvalue problems we encounter in the search for travelling waves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-10T14:28:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49R50",
      "47A75",
      "34L15",
      "35D05",
      "35J60"
    ],
    "keywords": [
      "non-standard eigenvalue problems",
      "laplacians",
      "nonlinear eigenvalue problems",
      "multi-parameter eigenvalue problems",
      "non-linear evolution pde"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1827G"
    }
  }
}