{
  "annotation_id": "49cad265-7804-44da-8c8b-a739c3673f9a",
  "date_created": "2026-02-17T05:53:08.713000Z",
  "date_modified": "2026-02-17T05:53:08.713000Z",
  "file_hash": "da836051cbee885d74abe6b54053027df6f97cea66eb361b22e22679e89b87a8",
  "private": false,
  "record": {
    "abstract": "We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation.",
    "arxiv_id": "2601.06623",
    "authors": [
      "Philip Korman"
    ],
    "categories": [
      "math.AP",
      "math.CA",
      "math.DS"
    ],
    "journal_ref": "Electron. J. Differential Equations 2024, Paper No. 09",
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Necessary and sufficient condition for existence at resonance for eigenvalues of multiplicity two",
    "url": "https://arxiv.org/abs/2601.06623",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ad1e906d-2e02-4c96-b62c-d699180e5e0b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}