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EnglishIn this paper we deal with the following fractional Kirchhoff problem [M(Rn×Rn|u(x)-u(y)|p|x-y|n+spdxdyp-1(-Δ)psu=f(x,u)+λ|u|r-2u in ω,u=0 in Rnω. Here ω ω ⊂ n is a smooth bounded open set with continuous boundary δω, p &insin; (1, +∞), s &insin; (0, 1), n > sp, (-Δ)ps is the fractional p-Laplacian, M is a Kirchhoff function, f is a continuous function with subcritical growth, λ is a nonnegative parameter and r > p*s where ps*-=np/n-sp is the fractional critical Sobolev exponent. By combining variational techniques and a truncation argument, we prove two existence results for this problem, provided that the parameter λ is sufficiently small.
| Titolo: | Supercritical fractional Kirchhoff type problems | |
| Autori: | ||
| Data di pubblicazione: | 2019 | |
| Rivista: | ||
| Abstract: | In this paper we deal with the following fractional Kirchhoff problem [M(Rn×Rn|u(x)-u(y)|p|x-y|n+spdxdyp-1(-Δ)psu=f(x,u)+λ|u|r-2u in ω,u=0 in Rnω. Here ω ω ⊂ n is a smooth bounded open set with continuous boundary δω, p &insin; (1, +∞), s &insin; (0, 1), n > sp, (-Δ)ps is the fractional p-Laplacian, M is a Kirchhoff function, f is a continuous function with subcritical growth, λ is a nonnegative parameter and r > p*s where ps*-=np/n-sp is the fractional critical Sobolev exponent. By combining variational techniques and a truncation argument, we prove two existence results for this problem, provided that the parameter λ is sufficiently small. | |
| Handle: | http://hdl.handle.net/11566/278516 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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