Nonlinear equations involving the square root of the LaplacianAmbrosio, Vincenzo (Avtor) Molica Bisci, Giovanni (Avtor) Repovš, Dušan (Avtor) fractional Laplacianvariational methodsmultiple solutionsIn 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.20192019-07-25 09:18:46Članek v reviji108787UDK: 517.951.6ISSN pri članku: 1937-1632DOI: 10.3934/dcdss.201901COBISS_ID: 18407513OceCobissID: 16098905sl