{
  "id": "2011.05654",
  "version": "v1",
  "published": "2020-11-11T09:27:03.000Z",
  "updated": "2020-11-11T09:27:03.000Z",
  "title": "Multiple solutions for asymptotically linear $(p,q)$-Laplacian problems",
  "authors": [
    "Francesca Colasuonno"
  ],
  "comment": "19 pages, 0 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the existence and the multiplicity of solutions of the problem $$ \\begin{cases} -\\Delta_p u-\\Delta_q u = g(x, u)\\quad & \\mbox{in } \\Omega,\\\\ \\displaystyle{u=0} & \\mbox{on } \\partial\\Omega, \\end{cases} $$ where $\\Omega$ is a smooth, bounded domain of $\\mathbb R^N$, $1<p<q<\\infty$, and the nonlinearity $g$ behaves as $u^{q-1}$ at infinity. We use variational methods and find multiple solutions as minimax critical points of the associated energy functional. Under suitable assumptions on the nonlinearity, we cover also the resonant case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T09:27:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple solutions",
      "laplacian problems",
      "asymptotically linear",
      "variational methods",
      "associated energy functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}