Infinitely many solutions for the stationary fractional p-Kirchhoff problems in RN
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer India
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In the present paper, we investigate the existence of multiple solutions for the nonhomogeneous fractional p-Kirchhoff equation M(integral integral R2N vertical bar u(x) - u(y)vertical bar(p)/vertical bar x - y vertical bar(N+ps)dxdy + integral V-RN(x)vertical bar u vertical bar p dx) x((-Delta)(p)(s) u + V(x) vertical bar u vertical bar(p-2) u) = f (x, u) in R-N, where (-Delta)(p)(s) is the fractional p-Laplacian operator, 0 < s < 1 < p < infinity with sp < N, M : R-0(+) -> R-0(+) is a nonnegative, continuous and increasing Kirchhoff function, the nonlinearity f : R-N x R -> R is a Caratheodory function that obeys some conditions which will be stated later and V is an element of C(R-N, R+) is a non-negative potential function. We first establish the Bartsch-Pankov-Wang type compact embedding theorem for the fractional Sobolev spaces. Then multiplicity results are obtained by using the variational method, (S+) mapping theory and Krasnoselskii's genus theory.
Açıklama
Anahtar Kelimeler
Kirchhoff equation, fractional p-Laplacian, variational methods, Krasnoselskii's genus, infinitely many solutions
Kaynak
Proceedings of the Indian Academy of Sciences-Mathematical Sciences
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
Cilt
129
Sayı
5
