Existence at least four solutions for a Schr "odinger equation with\n magnetic potential involving sign-changing weight function

2019/04/12 by Francisco Odair de Paiva, de Paiva, Francisco Odair Vieira, Sandra Machado de Souza Lima +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1904.06336

openalex publication_date 2019/04/12 · 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 , for x \∈\n\ℝ^N, 1<q<2<p<2^*-1= \(N+2)/(N-2), a_\λ(x) is a\nsign-changing weight function, b_\μ(x) has some aditional conditions, u\n\∈ H¹_A(\ℝ^N) and A:\ℝ^N \→\ℝ^N is a\nmagnetic potential. Exploring the Bahri Li argument and some preliminar results\nwe will discuss the existence of four solution to the problem in question.\n

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn

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