{
  "id": "1503.01807",
  "version": "v1",
  "published": "2015-03-05T22:25:33.000Z",
  "updated": "2015-03-05T22:25:33.000Z",
  "title": "Non-spurious solutions to discrete boundary value problems through variational methods",
  "authors": [
    "Marek Galewski",
    "Ewa Schmeidel"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\\ddot{x}\\left( t\\right) =f\\left( t,x\\left( t\\right) \\right) $, $x\\left( 0\\right) =x\\left( 1\\right) =0 $ where $f:\\left[ 0,1\\right] \\times \\mathbb{R} \\rightarrow \\mathbb{R}$ is a jointly continuous function convex in $x$ which does not need to satisfy any further growth conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-05T22:25:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A12",
      "39A10",
      "34B15"
    ],
    "keywords": [
      "discrete boundary value problems",
      "non-spurious solutions",
      "direct variational method",
      "growth conditions",
      "dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}