Infinitely Many Solutions for Schr?dinger–Choquard–Kirchhoff Equations Involving the Fractional p-Laplacian |
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基金项目: | Supported by National Natural Science Foundation of China (Grant No. 11701178) and Natural Science Foundation program of Jiangxi Provincial (Grant No. 20202BABL201011) and Natural Science Foundation of Jiangxi Educational Committee (Grant No. GJJ190337) |
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摘 要: | In this article,we show the existence of infinitely many solutions for the fractional pLaplacian equations of Schr?dinger-Kirchhoff type equation ■ ,where(-△)_p~s is the fractional p-Laplacian operator,u]_(s,p) is the Gagliardo p-seminorm,0 s 1 q p N/s,α∈(0,N),M and V are continuous and positive functions,and k(x) is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.
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Infinitely Many Solutions for Schrödinger-Choquard-Kirchhoff Equations Involving the Fractional p-Laplacian |
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Authors: | Li WANG Tao HAN Ji Xiu WANG |
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Institution: | 1. College of Science, East China Jiaotong University, Nanchang 330013, P. R. China;
2. School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053, P. R. China |
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Abstract: | In this article, we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrödinger-Kirchhoff type equation
M(u]s,pp)(-Δ)psu + V (x)|u|p-2u=λ(Iα *|u|ps,α*|u|ps,α*-2u + βk(x)|u|q-2u, x ∈ RN,
where (-Δ)ps is the fractional p-Laplacian operator,u]s,p is the Gagliardo p-seminorm, 0 < s < 1 < q < p < N/s, α ∈ (0, N), M and V are continuous and positive functions, and k(x) is a non-negative function in an appropriate Lebesgue space. Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β. |
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Keywords: | Schrö dinger-Choquard-Kirchhoff type fractional p-Laplacian variational methods critical Sobolev exponent |
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