We study the equation −Δgw+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.
Appolloni, L., Molica Bisci, G., Secchi, S. (2023). Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 519(2) [10.1016/j.jmaa.2022.126853].
Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities
Appolloni L.;Secchi S.
2023
Abstract
We study the equation −Δgw+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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