Multiplicity of concentrating solutions for (p, q)-Schrödinger equations with lack of compactness

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151291" target="_blank" >RIV/00216305:26220/24:PU151291 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007/s11856-024-2619-8.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s11856-024-2619-8.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11856-024-2619-8" target="_blank" >10.1007/s11856-024-2619-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiplicity of concentrating solutions for (p, q)-Schrödinger equations with lack of compactness

Popis výsledku v původním jazyce

We study the multiplicity of concentrating solutions for the following class of (p, q)-Laplacian problems (Formula presented.) where ε > 0 is a small parameter, γ∈{0,1},1<p<q<N,q∗=NqN−q is the critical Sobolev exponent, Δsu=div(∣∇u∣s−2∇u), with s ∈ {p, q}, is the s-Laplacian operator, V: ℝN → ℝ is a positive continuous potential such that inf∂ΛV > infΛV for some bounded open set Λ ⊂ ℝN, and f: ℝ → ℝ is a continuous nonlinearity with subcritical growth. The main results are obtained by combining minimax theorems, penalization technique and Ljusternik–Schnirelmann category theory. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. As far as we know, all these results are new.

Název v anglickém jazyce

Multiplicity of concentrating solutions for (p, q)-Schrödinger equations with lack of compactness

Popis výsledku anglicky

We study the multiplicity of concentrating solutions for the following class of (p, q)-Laplacian problems (Formula presented.) where ε > 0 is a small parameter, γ∈{0,1},1<p<q<N,q∗=NqN−q is the critical Sobolev exponent, Δsu=div(∣∇u∣s−2∇u), with s ∈ {p, q}, is the s-Laplacian operator, V: ℝN → ℝ is a positive continuous potential such that inf∂ΛV > infΛV for some bounded open set Λ ⊂ ℝN, and f: ℝ → ℝ is a continuous nonlinearity with subcritical growth. The main results are obtained by combining minimax theorems, penalization technique and Ljusternik–Schnirelmann category theory. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. As far as we know, all these results are new.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ISRAEL JOURNAL OF MATHEMATICS

ISSN

0021-2172

e-ISSN

1565-8511

Svazek periodika

262

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IL - Stát Izrael

Počet stran výsledku

49

Strana od-do

399-447

Kód UT WoS článku

001231083600008

EID výsledku v databázi Scopus

2-s2.0-85191882210