Nonlinear equations involving the square root of the Laplacian

Vincenzo Ambrosio (Avtor), Giovanni Molica Bisci (Avtor), Dušan Repovš (Avtor)

Povzetek

In this paper we discuss the existence and non-existence of weak solutions to parametric fractional equations involving the square root of the Laplacian ▫$A_{1/2}$▫ in a smooth bounded domain ▫$\Omega\subset \mathbb{R}^n$▫ (▫$n\geq 2$▫) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation ▫$$ \left\{ \begin{array}{ll} A_{1/2}u=\lambda f(u) & \mbox{ in } \Omega\\ u=0 & \mbox{ on } \partial\Omega. \end{array}\right. $$▫ The existence of at least two non-trivial ▫$L^{\infty}$▫-bounded weak solutions is established for large value of the parameter ▫$\lambda$▫ requiring that the nonlinear term ▫$f$▫ is continuous, superlinear at zero and sublinear at infinity. Our approach is based on variational arguments and a suitable variant of the Caffarelli-Silvestre extension method.

Ključne besede

fractional Laplacian;variational methods;multiple solutions;

Podatki

Jezik:	Angleški jezik
Leto izida:	2019
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.951.6
COBISS:	18407513
ISSN:	1937-1632
Št. ogledov:	520
Št. prenosov:	170
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 151-170
Letnik:	ǂVol. ǂ12
Zvezek:	ǂiss. ǂ2
Čas izdaje:	Apr. 2019
DOI:	10.3934/dcdss.2019011
ID:	11193865