{
  "id": "2409.03191",
  "version": "v1",
  "published": "2024-09-05T02:30:03.000Z",
  "updated": "2024-09-05T02:30:03.000Z",
  "title": "Stability and instability of constant stationary solutions to some integro-differential equations",
  "authors": [
    "Yuming Chen",
    "Vitali Vougalter"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of nontrivial constant stationary solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-05T02:30:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K57",
      "45K05"
    ],
    "keywords": [
      "integro-differential equations",
      "instability",
      "nontrivial constant stationary solutions",
      "reaction-diffusion equations",
      "nonlocal consumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}