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On a class of Kirchhoff problems via local mountain pass
ID Ambrosio, Vincenzo (Author), ID Repovš, Dušan (Author)

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Abstract
In the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: ▫$$\begin{cases}-(\varepsilon^2a+\varepsilon b\int _{\mathbb{R}^3}|\nabla u|^2 dx) \Delta u + V(x)u = f(u)+\gamma u^5 & \text{in} \; \mathbb{R}^3, \\ u \in H^1(\mathbb{R}^3), \quad u>0 & \text{in} \; \mathbb{R}^3, \end{cases}$$▫ where ▫$\varepsilon>0$▫ is a small parameter, ▫$a,b>0$▫ are constants, ▫$\gamma \in {0,1}$▫, ▫$V$▫ is a continuous positive potential with a local minimum, and ▫$f$▫ is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483-510; J. Differ. Equ. 252 (2012), 1813-1834; J. Differ. Equ. 253 (2012), 2314-2351).

Language:English
Keywords:Kirchhoff problems, penalization method, Ljusternik-Schnirelmann theory, critical growth, supercritical exponent
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:2022
Number of pages:Str. 1-43
Numbering:Vol. 126, iss.1-2
PID:20.500.12556/RUL-133972 This link opens in a new window
UDC:517.951
ISSN on article:0921-7134
DOI:10.3233/ASY-201660 This link opens in a new window
COBISS.SI-ID:43614723 This link opens in a new window
Publication date in RUL:21.12.2021
Views:425
Downloads:875
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Record is a part of a journal

Title:Asymptotic analysis
Shortened title:Asymptot. anal.
Publisher:IOS Press
ISSN:0921-7134
COBISS.SI-ID:25030144 This link opens in a new window

Projects

Funder:ARRS - Slovenian Research Agency
Project number:P1-0292
Name:Topologija, geometrija in nelinearna analiza

Funder:ARRS - Slovenian Research Agency
Project number:N1-0114
Name:Algebrajski odtisi geometrijskih značilnosti v homologiji

Funder:ARRS - Slovenian Research Agency
Project number:N1-0064
Name:Analiza zveznih in diskretnih matematičnih modelov v biologiji, kemiji in genetiki

Funder:ARRS - Slovenian Research Agency
Project number:J1-8131
Name:Zvezni in diskretni sistemi v nelinearni analizi

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