Vincenzo Ambrosio (Author), Dušan Repovš (Author)

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).

Keywords

Kirchhoff problems;penalization method;Ljusternik-Schnirelmann theory;critical growth;supercritical exponent;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956
COBISS: 43614723 Link will open in a new window
ISSN: 0921-7134
Views: 168
Downloads: 60
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Other data

Type (COBISS): Article
Pages: str. 1-43
Volume: ǂVol. ǂ126
Issue: ǂiss. ǂ1-2
Chronology: 2022
DOI: 10.3233/ASY-201660
ID: 14119068