In this paper, we deal with a Kirchhoff type problem driven by a nonlocal fractional integrodifferential operator L-K, that is, -M(parallel to u parallel to(2))LKu = lambda f(x, u) [integral(Omega) F(x, u(x))d(x)](r) + vertical bar u vertical bar(2*-2)u in Omega, u = 0 in R-n Omega, where Omega is an open bounded subset of R-n, M and f are continuous functions, parallel to center dot parallel to is a functional norm, F(x, u(x)) = integral(0) (u(x)) f(x, tau)d tau, 2* is a fractional Sobolev exponent, lambda and r are real parameters. For this problem, we prove the existence of infinitely many solutions, through a suitable truncation argument and exploiting the genus theory introduced by Krasnoselskii.

Fiscella, A. (2016). Infinitely many solutions for a critical Kirchhoff type problem involving a fractional operator. DIFFERENTIAL AND INTEGRAL EQUATIONS, 29(5-6), 513-530.

### Infinitely many solutions for a critical Kirchhoff type problem involving a fractional operator

#### Abstract

In this paper, we deal with a Kirchhoff type problem driven by a nonlocal fractional integrodifferential operator L-K, that is, -M(parallel to u parallel to(2))LKu = lambda f(x, u) [integral(Omega) F(x, u(x))d(x)](r) + vertical bar u vertical bar(2*-2)u in Omega, u = 0 in R-n Omega, where Omega is an open bounded subset of R-n, M and f are continuous functions, parallel to center dot parallel to is a functional norm, F(x, u(x)) = integral(0) (u(x)) f(x, tau)d tau, 2* is a fractional Sobolev exponent, lambda and r are real parameters. For this problem, we prove the existence of infinitely many solutions, through a suitable truncation argument and exploiting the genus theory introduced by Krasnoselskii.
##### Scheda breve Scheda completa Scheda completa (DC)
Articolo in rivista - Articolo scientifico
Kirchhoff type problems, fractional Laplacian, nonlocal problems, critical nonlinearities, variational methods, Krasnoselskii's genus
English
513
530
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Fiscella, A. (2016). Infinitely many solutions for a critical Kirchhoff type problem involving a fractional operator. DIFFERENTIAL AND INTEGRAL EQUATIONS, 29(5-6), 513-530.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/338142`
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