Existence, multiplicity and regularity for a Schr "odinger equation with\n magnetic potential involving sign-changing weight function

2019/04/15 by Francisco Odair de Paiva, de Paiva, Francisco Odair Vieira, Sandra Machado de Souza Lima +3
Mathematics · #35B33 #35B38 #35Q55 #35Q60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1904.07720

openalex publication_date 2019/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the following class of elliptic problems -\n
Delta_A u + u = a
_lambda(x) |u|^q-2u+b
_mu(x) |u|^p-2u ,
,
, x
in\n
mathbbR^N where 1<q<2<p<2^*-1= \(N+2)/(N-2), a_\λ(x) is a\nsign-changing weight function, b_\μ(x) have some aditional conditions, u\n\∈ H¹_A(\ℝ^N) and A:\ℝ^N \→\ℝ^N is a\nmagnetic potential. Exploring the relationship between the Nehari manifold and\nfibering maps, we will discuss the existence, multiplicity and regularity of\nsolutions.\n

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