The paper deals with the following singular fractional problem {M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dxdy) (-Delta)(s)u - mu u/vertical bar x vertical bar(2s) = lambda f(x)u(-gamma) + g(x)u(2s)*(-1) in Omega, u > 0 in Omega, u = 0 in R-nOmega, where Omega subset of R-N is an open bounded domain, with 0 is an element of Omega, dimension N > 2s with s is an element of (0, 1), 2(s)* = 2N/(N - 2s) is the fractional critical Sobolev exponent, lambda and mu are positive parameters, exponent gamma is an element of (0, 1), M models a Kirchhoff coefficient, f is a positive weight while g is a sign-changing function. The main feature and novelty of our problem is the combination of the critical Hardy and Sobolev nonlinearities with the bi-nonlocal framework and a singular nondifferentiable term. By exploiting the Nehari manifold approach, we provide the existence of at least two positive solutions.

Fiscella, A., Mishra, P. (2022). Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities. MANUSCRIPTA MATHEMATICA, 168(1-2), 257-301 [10.1007/s00229-021-01309-3].

Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities

Fiscella A
;
2022

Abstract

The paper deals with the following singular fractional problem {M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dxdy) (-Delta)(s)u - mu u/vertical bar x vertical bar(2s) = lambda f(x)u(-gamma) + g(x)u(2s)*(-1) in Omega, u > 0 in Omega, u = 0 in R-nOmega, where Omega subset of R-N is an open bounded domain, with 0 is an element of Omega, dimension N > 2s with s is an element of (0, 1), 2(s)* = 2N/(N - 2s) is the fractional critical Sobolev exponent, lambda and mu are positive parameters, exponent gamma is an element of (0, 1), M models a Kirchhoff coefficient, f is a positive weight while g is a sign-changing function. The main feature and novelty of our problem is the combination of the critical Hardy and Sobolev nonlinearities with the bi-nonlocal framework and a singular nondifferentiable term. By exploiting the Nehari manifold approach, we provide the existence of at least two positive solutions.
Articolo in rivista - Articolo scientifico
Kirchhoff type problems, Hardy terms, fractional Laplacian, singularities, Sobolev critical nonlinearities, Nehari manifolds;
English
257
301
45
Fiscella, A., Mishra, P. (2022). Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities. MANUSCRIPTA MATHEMATICA, 168(1-2), 257-301 [10.1007/s00229-021-01309-3].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/338126
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
Social impact