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Infinitely many sign-changing solutions for nonlinear fractional Kirchhoff equations
Applicable Analysis ( IF 1.1 ) Pub Date : 2021-03-31 , DOI: 10.1080/00036811.2021.1909722
Guangze Gu 1 , Xianyong Yang 2 , Zhipeng Yang 1, 3
Affiliation  

In this paper, we investigate the following fractional Kirchhoff equation: (a+bR3|(Δ)s2u|dx)(Δ)su+V(x)u=f(u),xR3,where a>0,b0, (Δ)s denotes the fractional Laplacian operator with order s(34,1), V is a positive continuous potential and f is supercubic but subcritical functional at infinity with some valid conditions. We prove that there exist multiple sign-changing solutions for the above problem via the method of invariant sets of descending flow. In particular, the nonlinear term includes the power-type nonlinearity f(u)=|u|p2u for the less studied case p(3,4). Even for s = 1, our result is new and extends the existing results in the literature.



中文翻译:

非线性分数基尔霍夫方程的无穷多符号变化解

在本文中,我们研究了以下分数基尔霍夫方程:(一个+bR3|(-Δ)s2|dX)(-Δ)s+(X)=F(),XR3,在哪里一个>0,b0,(-Δ)s表示带阶的分数拉普拉斯算子s(34,1), V是一个正连续势,f是超立方但在无穷远处具有一些有效条件的亚临界泛函。我们通过降流不变集的方法证明了上述问题存在多个符号变化解。特别是,非线性项包括幂型非线性F()=||p-2对于研究较少的案例p(3,4). 即使对于s  = 1,我们的结果也是新的,并且扩展了文献中的现有结果。

更新日期:2021-03-31
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