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Multiplicity and concentration of solutions for Kirchhoff equations with magnetic fieldJi, Chao ; Rǎdulescu, Vicenţiu, 1958-In this paper, we study the following nonlinear magnetic Kirchhoff equation: ▫$$ \begin{cases} -(a\epsilon^2 + b\epsilon[u]_{A/\epsilon}^2)\Delta_{A/\epsilon}u + V(x)u = f(|u|^2)u & \text{in} ... \;\mathbb{R}^3, \\ u \in H^1(\mathbb{R}^3,\mathbb{C}), \end{cases}$$▫ where ▫$\epsilon >0$▫, ▫$a,b>0$▫ are constants, ▫$V: \mathbb{R}^{3} \rightarrow \mathbb{R}$▫ and ▫$A: \mathbb{R}^3 \rightarrow \mathbb{R}^3$▫ are continuous potentials, and ▫$\Delta_A u$▫ is the magnetic Laplace operator. Under a local assumption on the potential ▫$V$▫, by combining variational methods, a penalization technique and the Ljusternik-Schnirelmann theory, we prove multiplicity properties of solutions and concentration phenomena for ▫$\epsilon$▫ small. In this problem, the function ▫$f$▫ is only continuous, which allows to consider larger classes of nonlinearities in the reaction.Source: Advanced nonlinear studies. - ISSN 1536-1365 (Vol. 21, iss. 3, 2021, str. 501-521)Type of material - article, component part ; adult, seriousPublish date - 2021Language - englishCOBISS.SI-ID - 64224771
Author
Ji, Chao |
Rǎdulescu, Vicenţiu, 1958-
Topics
Kirchhoff equation |
magnetic field |
concentration |
multiple solutions |
variational methods
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Ji, Chao | ![]() |
Rǎdulescu, Vicenţiu, 1958- | 29964 |
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