TY - JOUR
T1 - Existence and Multiplicity Results for a Class of Nonlinear Schrödinger Equations with Magnetic Potential Involving Sign-Changing Nonlinearity
AU - de Paiva , Francisco Odair
AU - Souza Lima , Sandra Machado de
AU - Miyagaki , Olimpio Hiroshi
JO - Analysis in Theory and Applications
VL - 2
SP - 148
EP - 177
PY - 2022
DA - 2022/07
SN - 38
DO - http://doi.org/10.4208/ata.OA-2021-0001
UR - https://global-sci.org/intro/article_detail/ata/20797.html
KW - Magnetic potential, sign-changing weight functions, Nehari manifold, Fibering map.
AB - <p style="text-align: justify;">In this work we consider the following class of elliptic problems $\begin{cases}&nbsp; −∆_Au + u = a(x)|u|^{q−2}u + b(x)|u|^{p−2}u &amp; {\rm in} &amp; \mathbb{R}^N, \\u ∈ H^1_A (\mathbb{R}^N),&nbsp; &nbsp;\tag{P} \end{cases}$ with $2 &lt; q &lt; p &lt; 2^∗ = \frac{2N}{N−2},$ $a(x)$ and $b(x)$ are functions that can change sign and satisfy some additional conditions; $u \in H^1_A (\mathbb{R}^N)$ and $A : \mathbb{R}^N → \mathbb{R}^N$ is a magnetic potential. Also using the Nehari method in combination with other complementary arguments, we discuss the existence of infinitely many solutions to the problem in question, varying the assumptions about the weight functions.</p>