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  • Existence of solutions for perturbed fractional ▫$p$▫-Laplacian equations
    Xiang, Mingqi ; Zhang, Binlin ; Rǎdulescu, Vicenţiu, 1958-
    The purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional ▫$p$▫-Laplacian operator as follows: ▫$$(-\Delta)_p^s ... u + V(x)|u|^{p-2}u = \lambda a(x) |u|^{r-2}u-b(x)|u|^{q-2}u \quad \text{in} \quad \mathbb{R}^N,$$▫ where ▫$\lambda$▫ is a real parameter, ▫$(-\Delta)_p^s$▫ is the fractional ▫$p$▫-Laplacian operator with ▫$0 < s < 1 < p < \infty$▫, ▫$p < r < \min \{q, p_s^\ast \}$▫ and ▫$V, a, b \colon \mathbb{R}^N \to(0, \infty)$▫ are three positive weights. Using variational methods, we obtain nonexistence and multiplicity results for the above-mentioned equations depending on ▫$\lambda$▫ and according to the integrability properties of the ratio ▫$a^{q-p} / b^{r-p}$▫. Our results extend the previous work of Autuori and Pucci [G. Autuori, P. Pucci, Elliptic problems involving the fractional Laplacian in ▫$\mathbb{R}^N$▫, J.Differential Equations 255 (2013) 2340-2362] to the fractional ▫$p$▫-Laplacian setting. Furthermore, we weaken one of the conditions used in their paper. Hence the results of this paper are new even in the fractional Laplacian case.
    Vir: Journal of differential equations. - ISSN 0022-0396 (Vol. 260, iss. 2, 2016, str. 1392-1413)
    Vrsta gradiva - članek, sestavni del
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 17523545

    Povezava(-e):

    http://dx.doi.org/10.1016/j.jde.2015.09.028

vir: Journal of differential equations. - ISSN 0022-0396 (Vol. 260, iss. 2, 2016, str. 1392-1413)

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