Multiple solutions of nonlinear equations involving the square root of the Laplacian

Molica Bisci, Giovanni (avtor), Repovš, Dušan (avtor), Vilasi, Luca (avtor)

In this paper, we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian $A_{1/2}$ in a smooth bounded domain $\Omega \subset \mathbb{R}^n$ $(n \ge 2)$ and with Dirichlet zero-boundary conditions, i.e. $$ \begin{cases} A_{1/2}u = \lambda f(u) & \text{in} \quad \Omega \\ u = 0 & \text{on} \quad \partial \Omega. \end{cases}$$ The existence of at least three $L^\infty$-bounded weak solutions is established for certain values of the parameter $\lambda$ requiring that the nonlinear term $f$ is continuous and with a suitable growth. Our approach is based on variational arguments and a variant of Caffarelli-Silvestre's extension method.

• Jezik: Angleški jezik
• Ključne besede: fractional Laplacian, variational method, multiple solutions
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2017
• Št. strani: Str. 1483-1496
• Številčenje: Vol. 96, no. 9
• PID: 20.500.12556/RUL-109675
• UDK: 517.95
• ISSN pri članku: 0003-6811
• DOI: 10.1080/00036811.2016.1221069
• COBISS.SI-ID: 17736793
• Datum objave v RUL: 06.09.2019

MOLICA BISCI, Giovanni, REPOVŠ, Dušan in VILASI, Luca, 2017, Multiple solutions of nonlinear equations involving the square root of the Laplacian. Applicable analysis [na spletu]. 2017. Vol. 96, no. 9, p. 1483–1496. [Dostopano 14 junij 2025]. DOI 10.1080/00036811.2016.1221069. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109675

Gradivo je del revije

• Naslov: Applicable analysis
• Skrajšan naslov: Appl. anal.
• Založnik: Taylor & Francis
• ISSN: 0003-6811
• COBISS.SI-ID: 24981760