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• W3100759434 abstract "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 $Omegasubset mathbb{R}^n$ ($ngeq 2$) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation begin{equation*} left{ begin{array}{ll} A_{1/2}u=lambda f(u) & mbox{ in } Omega u=0 & mbox{ on } partialOmega. end{array}right. end{equation*} 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." @default.
• W3100759434 created "2020-11-23" @default.
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• W3100759434 date "2019-01-01" @default.
• W3100759434 modified "2023-10-18" @default.
• W3100759434 title "Nonlinear equations involving the square root of the Laplacian" @default.
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• W3100759434 doi "https://doi.org/10.3934/dcdss.2019011" @default.
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