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Infinitely many sign-changing solutions for Choquard equation with doubly critical exponents
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-10-02 , DOI: 10.1080/17476933.2020.1825394
Senli Liu 1 , Jie Yang 1 , Haibo Chen 1
Affiliation  

In this paper, we consider the following Choquard equation: Δu+u=(IαF(u))F(u)in RN where N3, α(0,N), Iα is the Riesz potential, and F(u):=1p|u|p+1q|u|q, where p=N+αN and q=N+αN2 are lower and upper critical exponents in sense of the Hardy–Littlewood–Sobolev inequality. Based on perturbation method and the invariant sets of descending flow, we prove that the above equation possesses infinitely many sign-changing solutions. Our results extend the results in Seok [Nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2018;76:148–156] and Su [New result for nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2020;102(106092):0–7].



中文翻译:

具有双临界指数的 Choquard 方程的无穷多符号变化解

在本文中,我们考虑以下 Choquard 方程:-Δ+=(一世α*F())F'()一世n Rñ在哪里ñ3,α(0,ñ),一世α是 Riesz 势,并且F():=1p||p+1q||q, 在哪里p=ñ+αñq=ñ+αñ-2是 Hardy-Littlewood-Sobolev 不等式意义上的下临界指数和上临界指数。基于摄动法和下行流的不变集,我们证明了上述方程具有无穷多个变号解。我们的结果扩展了 Seok [非线性 Choquard 方程:双重临界情况。应用数学莱特。2018;76:148–156] 和 Su [非线性 Choquard 方程的新结果:双重临界情况。应用数学莱特。2020;102(106092):0-7]。

更新日期:2020-10-02
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