Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities

2022/09/19 by Appolloni, Luigi, Bisci, Giovanni Molica, Secchi, Simone
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.08852

Abstract

We study the equation -Δ_g w+w=λα(σ) f(w) on a d-dimensional homogeneous Cartan-Hadamard Manifold M with d ≥ 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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