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

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

Povzetek

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.

Ključne besede

fractional Laplacian;variational method;multiple solutions;

Podatki

Jezik:	Angleški jezik
Leto izida:	2017
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.95
COBISS:	17736793
ISSN:	0003-6811
Št. ogledov:	511
Št. prenosov:	341
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 1483-1496
Letnik:	ǂVol. ǂ96
Zvezek:	ǂno. ǂ9
Čas izdaje:	2017
DOI:	10.1080/00036811.2016.1221069
ID:	11217776