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  • Nonlinear equations involving the square root of the Laplacian
    Ambrosio, Vincenzo, 1986- ; Molica Bisci, Giovanni, 1975- ; Repovš, Dušan, 1954-
    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.
    Source: Discrete and continuous dynamical systems. Series S. - ISSN 1937-1632 (Vol. 12, iss. 2, Apr. 2019, str. 151-170)
    Type of material - article, component part ; adult, serious
    Publish date - 2019
    Language - english
    COBISS.SI-ID - 18407513

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