The Nehari Manifold for a Fractional p-Kirchhoff System Involving Sign-Changing Weight Function and Concave-Convex Nonlinearities

The Nehari Manifold for a Fractional p-Kirchhoff System Involving Sign-Changing Weight Function and Concave-Convex Nonlinearities

In this paper, we are concerned with the following fractional p-Kirchhoff system with sign-changing nonlinearities: M(∫R2nux-uyp/x-yn+psdxdy)-Δpsu=λa(x)uq-2u+α/(α+β)f(x)uα-2uvβ, in Ω, M(∫R2n|v(x)-v(y)|p/|x-y|n+psdxdy)-Δpsv=μb(x)vq-2v+(β/α+β)f(x)uαvβ-2v, in Ω, and u=v=0, in Rn∖Ω, where Ω is a smooth...

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Veröffentlicht in:Journal of function spaces 2019-01, Vol.2019 (2019), p.1-9
Hauptverfasser: Ren, Xiangsheng, Yang, Libo, An, Tianqing, Zuo, Jiabin
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Banach spaces
Continuity (mathematics)
Manifolds
Parameters
Partial differential equations
Weighting functions
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Zusammenfassung:In this paper, we are concerned with the following fractional p-Kirchhoff system with sign-changing nonlinearities: M(∫R2nux-uyp/x-yn+psdxdy)-Δpsu=λa(x)uq-2u+α/(α+β)f(x)uα-2uvβ, in Ω, M(∫R2n|v(x)-v(y)|p/|x-y|n+psdxdy)-Δpsv=μb(x)vq-2v+(β/α+β)f(x)uαvβ-2v, in Ω, and u=v=0, in Rn∖Ω, where Ω is a smooth bounded domain in Rn, n>ps, s∈(0,1), λ, μ are two real parameters, 1
ISSN:2314-8896
2314-8888
DOI:10.1155/2019/7624373