20.500.12556/RUL-109675 Multiple solutions of nonlinear equations involving the square root of the Laplacian 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. fractional Laplacian variational method multiple solutions true false true Angleški jezik Ni določen Članek v reviji 2019-09-06 14:17:48 2019-09-06 14:17:50 2022-08-21 03:43:44 0000-00-00 00:00:00 2017 0 0 Str. 1483-1496 no. 9 Vol. 96 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.95 0003-6811 10.1080/00036811.2016.1221069 17736793 24981760 RAZ_Molica_Bisci_Giovanni_i2017.pdf RAZ_Molica_Bisci_Giovanni_i2017.pdf 1 B5AECE1844946D67D10FE823695581FF bb00a83c76775372d68b2ba344879173f88f1311c7bb599c60c78a696b320b8e ed139990-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121262 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0