Fractional Laplacian equations with critical Sobolev exponent

By Raffaella Servadei, Enrico Valdinoci. 2015

96 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ff4f0d1fb0d57d6267965d4f99cad037620e49fb

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN (2016, background): “A Brézis–Nirenberg-type result for the nonlocal fractional Laplacian in bounded domainwith homogeneous Dirichlet boundary datum is given in [37] by variational techniques; see also [36] for further results.”
A critical fractional equation with concave-convex power nonlinearities (2013, methodology): “The linear case q 1, when the right hand side of the equation is equal to λu u s − 2 u , was treated in [37,38, 41–43 .”
Superlinear Schrödinger–Kirchhoff type problems involving the fractional p–Laplacian and critical exponent (2019, methodology): “For example, by variational techniques, Servadei and Valdinoci [4] showed a Brézis–Nirenberg type result for non-local fractional Laplacian in bounded domains with homogeneous Dirichlet boundary datum, see also [5] for further discussions.”
Bifurcation and multiplicity results for critical fractional p‐Laplacian problems (2014, result): “er [7] (see, e.g., [10, 9, 1, 23, 19, 38, 11, 15, 20, 22, 21, 12, 36] and references therein). Consequently, many results known in the local case s = 1 have been extended to problem (1.4) (see, e.g., [34, 31, 35, 32, 33, 2, 5, 37, 17]). In particular, 2 Fiscella et al. [17] have recently obtained th”
A bifurcation result for non-local fractional equations (2015, background): “In [4] [7] [8] [11] [19] [20] [21] [23] [24] [25] [26] [27] [30] (see also the references therein) the authors studied non-local fractional Laplacian equations with superlinear and subcritical or critical nonlinearities, while in [12] [13] the asymptotically linear case was exploited.”
Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials (2016, background): “Last but not least, fractional elliptic problems with critical growth, in a bounded domain, have been studied by some authors in the last years, see [6, 7, 18, 28, 39, 41] and references therein.”