arXiv subjects

Sandra Machado de Souza Lima

Publications and source records attributed to Sandra Machado de Souza Lima.

3 recordsLinked to original sources

arXiv2019

Existence, multiplicity and regularity for a Schrödinger equation with magnetic potential involving sign-changing weight function

In this paper we consider the following class of elliptic problems $$- Δ_A u + u = a_λ(x) |u|^{q-2}u+b_μ(x) |u|^{p-2}u ,\,\, x\in \mathbb{R}^N$$ where $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_λ(x)$ is a sign-changing weight function, $b_μ(x)$ have some aditional conditions, $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow\mathbb{R}^N$ is a magnetic potential. Exploring the relationship between the Nehari manifold and fibering maps, we will discuss the existence, multiplicity and regularity of solutions.

math.AP↗

arXiv2019

Existence at least four solutions for a Schrödinger equation with magnetic potential involving sign-changing weight function

In this paper we consider the following class of elliptic problems $$- Δ_A u + u = a_λ(x) |u|^{q-2}u+b_μ(x) |u|^{p-2}u ,$$ for $x \in \mathbb{R}^N$, $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_λ(x)$ is a sign-changing weight function, $b_μ(x)$ has some aditional conditions, $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow\mathbb{R}^N$ is a magnetic potential. Exploring the Bahri Li argument and some preliminar results we will discuss the existence of four solution to the problem in question.

math.AP↗

arXiv2019

Existence and multiplicity results for a class of non-linear Schrödinger equations with magnetic potential involving sign-changing non linearity

In this work we consider the following class of elliptic problems $$- Δ_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$ $u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and $b(x)$ are functions that can change signal and satisfy some additional conditions; $u \in H^1_A(\mathbb{R}^N)$ and $A:\mathbb{R}^N \rightarrow \mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in combination with other complementary arguments, we discuss the existence of infinite solutions to the problem in question, varying the assumptions about the weight functions.

math.AP↗