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  • Fractional double-phase patterns: concentration and multiplicity of solutions
    Ambrosio, Vincenzo, 1986- ; Rǎdulescu, Vicenţiu, 1958-
    We consider the following class of fractional problems with unbalanced growth: ▫$$ \begin{cases} (-\Delta)_p^su+(-\Delta)_q^su+V(\varepsilon x)(|u|^{p-2}u+|u|^{q-2}u)=f(u)\quad & \text{in ... }\mathbb{R}^N, \\ u\in W^{s,p}(\mathbb{R}^N)\cap W^{s,q}(\mathbb{R}^N),\quad u > 0 \quad & \text{in }\mathbb{R}^N, \end{cases} $$▫ where ▫$\varepsilon>0$▫ is a small parameter, ▫$s\in(0,1)$▫, ▫$2\leq p<q<\frac{N}{s}$▫, ▫$(-\Delta)_t^s$▫ (with ▫$t\in\{p,q\})$▫ is the fractional ▫$t$▫-Laplacian operator, ▫$V:\mathbb{R}^N\to\mathbb{R}$▫ is a continuous potential satisfying local conditions, and ▫$f:\mathbb{R}\to\mathbb{R}$▫ is a continuous nonlinearity with subcritical growth. Applying suitable variational and topological arguments, we obtain multiple positive solutions for ▫$\varepsilon>0$▫ sufficiently small as well as related concentration properties, in relationship with the set where the potential ▫$V$▫ attains its minimum.
    Vir: Journal de Mathématiques Pures et Appliquées. - ISSN 0021-7824 (Vol. 142, Oct. 2020, str. 101-145)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 30926083

    Povezava(-e):

    https://doi.org/10.1016/j.matpur.2020.08.011
    DOI

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