1/2-Laplacian problems with exponential nonlinearity

By Antonio Iannizzotto, Marco Squassina. 2013

106 citations recorded by the source corpus.

Abstract By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/678df51c8678f18d2aaaf512d6f677a7a7245f95

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Fractional Adams–Moser–Trudinger type inequalities (2015, background): “One can also prove existence results for more general semilinear equations, say (−∆) n 2 u = f(u) in Ω (27) with u ∈ H̃ n 2 (Ω) and f critical or subcritical, in the spirit for instance of the works of Adimurthi [4] and Iannizzotto and Squassina [23], even in the case of the fractional p-Laplacian, ”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “for x ∈ R , see [16,18–20] and the references therein for further details on the fractional p-Laplacian operator.”
Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation (2018, background): “Furthermore, do Ó,Miyagaki and Squassina [17, 18] overcame the possible failure of the lack of compactness and investigated the existence of ground state solutions to the following problem:−Cs2 ∫ ℝ u(x + y) + u(x − y) − 2u(x)|y|1+2s dy + u = f(u), u ∈ W 12 ,20 (ℝ).”
Existence results for fractional p-Laplacian problems via Morse theory (2014, methodology): “Several existence results via variational methods are proved in a series of papers of Servadei andValdinoci [41–43, 45] (see also Iannizzotto andSquassina [21] for the special case s = 1/2,p = 2 andN = 1, with exponential nonlinearity).”