Schr\"odinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

Luigi Appolloni; Giovanni Molica Bisci; Simone Secchi

Schr\"odinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

Analysis of PDEs 2022-09-20 v1

Authors: Luigi Appolloni , Giovanni Molica Bisci , Simone Secchi

Abstract

We study the equation $-\Delta_g w+w=\lambda \alpha(\sigma) f(w)$ on a $d$ -dimensional homogeneous Cartan-Hadamard Manifold $\mathcal{M}$ with $d \geq 3$ . Without using the theory of topological indices, we prove the existence of infinitely many solutions for a class of nonlinearities $f$ which have an oscillating behavior either at zero or at infinity.

Keywords

schrodinger equation cartan-hadamard manifold oscillating nonlinearities infinitely many solutions existence of solutions

Cite

@article{arxiv.2209.08852,
  title  = {Schr\"odinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities},
  author = {Luigi Appolloni and Giovanni Molica Bisci and Simone Secchi},
  journal= {arXiv preprint arXiv:2209.08852},
  year   = {2022}
}

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