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  • Existence results for Kirchhoff-type superlinear problems involving the fractional Laplacian
    Zhang, Binlin ; Rǎdulescu, Vicenţiu, 1958- ; Wang, Li, matematik
    In this paper, we study the existence and multiplicity of solutions for Kirchhoff-type superlinear problems involving non-local integro-differential operators. As a particular case, we consider the ... following Kirchhoff-type fractional Laplace equation: ▫$$\begin{cases} M\Big(\iint_{\mathbb{R}^{2N}} \frac{|u(x)-u(y)|^2}{|x-y|^{N}+2s}dxdy \Big) ( - \Delta)^s u= f(x,u) & \text{in} \quad\Omega \; , \\ u=0 & \text{in} \quad \mathbb{R}^N \setminus \Omega \; , \end{cases}$$▫ where ▫$( - \Delta)^s$▫ is the fractional Laplace operator, ▫$s \in (0, 1)$▫, ▫$N > 2s$▫, ▫$\Omega$▫ is an open bounded subset of ▫$\mathbb{R}^N$▫ with smooth boundary ▫$\partial \Omega$, $M \colon \mathbb{R}^+_0 \to \mathbb{R}^+$▫ is a continuous function satisfying certain assumptions, and ▫$f(x, u)$▫ is superlinear at infinity. By computing the critical groups at zero and at infinity, we obtain the existence of non-trivial solutions for the above problem via Morse theory. To the best of our knowledge, our results are new in the study of Kirchhoff-type Laplacian problems.
    Vir: Proceedings. Section A, Mathematics. - ISSN 0308-2105 (Vol. 149, iss. 4, Aug. 2019, str. 1061-1081)
    Vrsta gradiva - članek, sestavni del
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18514521

    Povezava(-e):

    https://doi.org/10.1017/prm.2018.105

    Omejena dostopnost


    DOI

vir: Proceedings. Section A, Mathematics. - ISSN 0308-2105 (Vol. 149, iss. 4, Aug. 2019, str. 1061-1081)
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