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arXiv · 2209.08852

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

Luigi Appolloni·Giovanni Molica Bisci·Simone Secchi
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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.

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Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi. 2022-09-19. Schr\"odinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities. https://arxiv.org/abs/2209.08852

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