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  • Multiplicity results for nonlocal fractional ▫$p$▫-Kirchhoff equations via Morse theory
    Zhang, Binlin ; Molica Bisci, Giovanni, 1975- ; Xiang, Mingqi
    In this paper, we apply Morse theory and local linking to study the existence of nontrivial solutions for Kirchhoff type equations involving the nonlocal fractional ▫$p$▫-Laplacian with homogeneous ... Dirichlet boundary conditions: ▫$$\begin{cases} \!\bigg[M\bigg(\displaystyle\iint_{\mathbb{R}^{2N}}\!\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\bigg)\bigg]^{p-1} \!(-\Delta)_p^su(x)=f(x,u)&\mbox{in }\Omega,\\ u=0&\mbox{in } \mathbb{R}^{N}\setminus\Omega, \end{cases}$$▫ where ▫$\Omega$▫ is a smooth bounded domain of ▫$\mathbb{R}^N$▫, ▫$(-\Delta)_p^s$▫ is the fractional ▫$p$▫-Laplace operator with ▫$0< s< 1< p< \infty$▫ with ▫$sp< N$▫, ▫$M \colon \mathbb{R}^{+}_{0}\rightarrow \mathbb{R}^{+}$▫ is a continuous and positive function not necessarily satisfying the increasing condition and ▫$f$▫ is a Carathéodory function satisfying some extra assumptions.
    Vir: Topological Methods in Nonlinear Analysis. - ISSN 1230-3429 (Vol. 49, no. 2, June 2017, str. 445-461)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 18015577

    Povezava(-e):

    http://dx.doi.org/10.12775/TMNA.2016.081
    DOI

vir: Topological Methods in Nonlinear Analysis. - ISSN 1230-3429 (Vol. 49, no. 2, June 2017, str. 445-461)

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