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  • A critical fractional equation with concave-convex power nonlinearities
    Barrios, Begoña ...
    In this work we study the following fractional critical problem ▫$$ (P_{\lambda})=\left\{\begin{array}{ll} (-\Delta)^s u=\lambda u^{q} + u^{2^*_{s}-1}, \quad u{>}0 & \mbox{in} \quad \Omega\\ u=0 & ... \mbox{in} \quad \mathbb R^n\setminus \Omega\,, \end{array}\right. $$▫ where ▫$\Omega\subset \mathbb{R}^n$▫ is a regular bounded domain, ▫$\lambda>0$▫, ▫$0<s<1$▫ and ▫$n>2s$▫. Here ▫$(-\Delta)^s$▫ denotes the fractional Laplace operator defined, up to a normalization factor, by ▫$$ -(-\Delta)^s u(x)= \int_{\mathbb R^n}\frac{u(x+y)+u(x-y)-2u(x)}{|y|^{n+2s}}\,dy, \quad x\in \mathbb R^n. $$▫ Our main results show the existence and multiplicity of solutions to problem ▫$(P_\lambda)$▫ for different values of ▫$\lambda$▫. The dependency on this parameter changes according to whether we consider the concave power case (▫$0<q<1$▫) or the convex power case (▫$1<q<2^*_s-1$▫). These two cases will be treated separately.
    Vir: Annales de l Institut Henri Poincare. Analyse non lineaire. - ISSN 0294-1449 (Vol. 32, iss. 4, 2015, str. 875-900)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17462617

    Povezava(-e):

    http://dx.doi.org/10.1016/j.anihpc.2014.04.003

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