| 次临界分数阶Laplace方程具有两个bubbles的变号解存在性 |
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| 引用本文： | 郭千桥,胡云云.次临界分数阶Laplace方程具有两个bubbles的变号解存在性[J].数学学报,2016,59(5):659-676. |
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| 作者姓名： | 郭千桥 胡云云 |
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| 作者单位： | 西北工业大学应用数学系 西安 710129 |
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| 基金项目： | 国家自然科学基金（11271299，11001221）；中央高校基本科研业务费资助项目（3102015ZY069） |
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| 摘 要： | 考虑次临界分数阶Laplace问题{(-△)~su=︳u︳~(p-1-ε)u,x∈Ω,u=0,x∈?Ω}具有两个bubbles的变号解的存在性,其中Ω是R~N中的有界光滑区域,N2s,0s1,p=(N+2s)/(N-2s),ε0充分小.这个工作可以看作Bartsch,Micheletti,Pistoia在文On the existence and the profile of nodal solutions of elliptic equations involving critical growth,Calc.Var.Partial Differential Equations,2006,3:265-282]结果的一种非局部形式的推广.
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| 关 键 词： | 分数阶Laplauce方程 变号解 次临界问题 |
Two-Bubble Nodal Solutions for Slightly Subcritical Fractional Laplacian |
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| Qian Qiao GUO,Yun Yun HU.Two-Bubble Nodal Solutions for Slightly Subcritical Fractional Laplacian[J].Acta Mathematica Sinica,2016,59(5):659-676. |
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| Authors: | Qian Qiao GUO Yun Yun HU |
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| Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, P. R. China |
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| Abstract: | We consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian
 (-△)su=|u|p-1-εu，x∈Ω，
 u=0，x∈∂Ω
where Ω is a smooth bounded domain in RN, N>2s, 0< s< 1, p=N+2s/N-2s and ε>0 is a small parameter, which can be seen as a nonlocal analog of the results of Bartsch, Micheletti, PistoiaOn the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Differential Equations, 2006, 3:265-282]. |
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| Keywords: | fractional Laplacian nodal solutions slightly subcritical problem |
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