VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Some existence results for variational inequalities with nonlocal fractional operators
    Pimenta, Marcos Tadeu Oliveira ; Servadei, Raffaella, 1973-
    In this paper we consider the following nonlocal fractional variational inequality ▫$$\begin{cases} u \in X^\delta_0(\Omega); \, u \leqslant \psi \; \text{a.e. in} \ \Omega,\\ \langle u,v - u ... \rangle_{X^\delta_0(\Omega)} - \lambda \langle u,v - u \rangle_2 \geqslant \int_\Omega f \bigl(x, u(x), (-\Delta)^\beta u(x)\bigr) (v(x)-u(x)) dx \\ \text{where for any} \, v \in X^\delta_0(\Omega), \, \psi \; \text{a.e. in} \, \Omega, \end{cases}$$▫ ▫$\Omega \subset \mathbb{R}^N$▫ is a smooth bounded open set with continuous boundary ▫$\partial \Omega$▫, ▫$s \in (0, 1)$▫, ▫$N>2s$▫, ▫$\lambda$▫ is a real parameter, ▫$f$▫ is function with subcritical growth, ▫$\beta \in (0, s/2)$▫ and is the obstacle function. As it is well-known, the dependence of the nonlinearity on the term ▫$(-\Delta)^\beta u$▫ makes non-variational the nature of this problem. Using an iterative technique and a penalization method, we get the existence of a nontrivial nonnegative solution for the problem under consideration, performing the Mountain Pass Theorem. This result can be seen as the extension of known existence theorem for variational inequalities driven by the Laplace operator (or more general uniformly elliptic operators) to the nonlocal fractional setting.
    Vir: Nonlinear Analysis. Theory, Methods and Applications. - ISSN 0362-546X (Vol. 189, Dec. 2019, art. 111561 [17 str.])
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18701145

    Povezava(-e):

    https://doi.org/10.1016/j.na.2019.06.020
    DOI

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