We consider a smooth, complete and non-compact Riemannian manifold (M, g) of dimension d≥ 3 , and we look for solutions to the semilinear elliptic equation -Δgw+V(σ)w=α(σ)f(w)+λwinM.The potential V: M→ R is a continuous function which is coercive in a suitable sense, while the nonlinearity f has a subcritical growth in the sense of Sobolev embeddings. By means of ∇ -theorems introduced by Marino and Saccon, we prove that at least three non-trivial solutions exist as soon as the parameter λ is sufficiently close to an eigenvalue of the operator - Δg.

Appolloni, L., Molica Bisci, G., Secchi, S. (2023). Multiple solutions for Schrödinger equations on Riemannian manifolds via ∇ -theorems. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 63(1) [10.1007/s10455-023-09885-1].

Multiple solutions for Schrödinger equations on Riemannian manifolds via ∇ -theorems

Appolloni L.;Secchi S.
2023

Abstract

We consider a smooth, complete and non-compact Riemannian manifold (M, g) of dimension d≥ 3 , and we look for solutions to the semilinear elliptic equation -Δgw+V(σ)w=α(σ)f(w)+λwinM.The potential V: M→ R is a continuous function which is coercive in a suitable sense, while the nonlinearity f has a subcritical growth in the sense of Sobolev embeddings. By means of ∇ -theorems introduced by Marino and Saccon, we prove that at least three non-trivial solutions exist as soon as the parameter λ is sufficiently close to an eigenvalue of the operator - Δg.
Articolo in rivista - Articolo scientifico
Riemannian manifolds; Schrödinger equations; Variational methods; ∇ -theorems;
English
24-gen-2023
2023
63
1
11
none
Appolloni, L., Molica Bisci, G., Secchi, S. (2023). Multiple solutions for Schrödinger equations on Riemannian manifolds via ∇ -theorems. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 63(1) [10.1007/s10455-023-09885-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/408397
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