Note on elliptic equations on closed manifolds with singular nonlinearities

Bartosz Bieganowski; Adam Konysz

Note on elliptic equations on closed manifolds with singular nonlinearities

Analysis of PDEs 2025-05-01 v1

Authors: Bartosz Bieganowski , Adam Konysz

Abstract

We consider a general elliptic equation $-\Delta_g u+V(x)u=f(x,u)+g(x,u^2)u$ on a closed Riemannian manifold $(M, g)$ and utilize a recent variational approach by Hebey, Pacard, Pollack to show the existence of a nontrivial solution under general assumptions on nonlinear terms $f$ and $g$ .

Keywords

semilinear elliptic equations positive solutions of elliptic equations elliptic partial differential equations

Cite

@article{arxiv.2504.21339,
  title  = {Note on elliptic equations on closed manifolds with singular nonlinearities},
  author = {Bartosz Bieganowski and Adam Konysz},
  journal= {arXiv preprint arXiv:2504.21339},
  year   = {2025}
}

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