Nehari manifold for a Schrödinger equation with magnetic potential involving sign-changing weight function

We consider the following class of elliptic problems \[ - \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\quad x\in {\mathbb{R}}^N, \] − Δ A u + u = a λ ( x ) | u | q − 2 u + b μ ( x ) | u | p − 2 u , x ∈ R N , where $ 1 0 are real parameters, $ u \in H^1_A({\mathbb {R}}^N) $ u ∈...

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Bibliographic Details
Published in:Applicable analysis 2024-04, Vol.103 (6), p.1036-1063
Main Authors: de Paiva, Francisco Odair, de Souza Lima, Sandra Machado, Miyagaki, Olímpio Hiroshi
Format: Article
Language:English
Subjects:
fibering map
magnetic potential
Manifolds
Nehari manifold
Schrodinger equation
Sign-changing weight function
Weighting functions
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Summary:We consider the following class of elliptic problems \[ - \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\quad x\in {\mathbb{R}}^N, \] − Δ A u + u = a λ ( x ) | u | q − 2 u + b μ ( x ) | u | p − 2 u , x ∈ R N , where $ 1 0 are real parameters, $ u \in H^1_A({\mathbb {R}}^N) $ u ∈ H A 1 ( R N ) and $ A:{\mathbb {R}}^N \rightarrow {\mathbb {R}}^N $ A : R N → R N is a magnetic potential. Exploring the relationship between the Nehari manifold and fibering maps, we will discuss the existence, multiplicity and regularity of solutions.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2023.2230257