{
  "id": "2502.03355",
  "version": "v1",
  "published": "2025-02-05T16:51:59.000Z",
  "updated": "2025-02-05T16:51:59.000Z",
  "title": "Solutions to general elliptic equations on nearly geodesically convex domains with many critical points",
  "authors": [
    "Alberto Enciso",
    "Francesca Gladiali",
    "Massimo Grossi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider a complete $d$-dimensional Riemannian manifold $(\\mathcal M,g)$, a point $p\\in\\mathcal M$ and a nonlinearity $f(q,u)$ with $f(p,0)>0$. We prove that for any odd integer $N\\ge3$, there exists a sequence of smooth domains $\\Omega_k\\subset\\mathcal M$ containing $p$ and corresponding positive solutions $u_k:\\Omega_k\\to\\R^+$ to the Dirichlet boundary problem",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-05T16:51:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general elliptic equations",
      "geodesically convex domains",
      "critical points",
      "dirichlet boundary problem",
      "dimensional riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}