Solutions to general elliptic equations on nearly geodesically convex domains with many critical points

Alberto Enciso; Francesca Gladiali; Massimo Grossi

Solutions to general elliptic equations on nearly geodesically convex domains with many critical points

Analysis of PDEs 2025-02-06 v1

Authors: Alberto Enciso , Francesca Gladiali , Massimo Grossi

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

Keywords

elliptic equations geodesically convex domains critical points Dirichlet problem Riemannian manifold

Cite

@article{arxiv.2502.03355,
  title  = {Solutions to general elliptic equations on nearly geodesically convex domains with many critical points},
  author = {Alberto Enciso and Francesca Gladiali and Massimo Grossi},
  journal= {arXiv preprint arXiv:2502.03355},
  year   = {2025}
}

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