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带临界指数的奇异椭圆方程Neumann问题多重解的存在性

, PP. 79-87

Keywords: Neumann问题&searchField=keyword">Neumann问题')"href="#">Neumann问题,Sobolev-Hardy临界指数,(PS)_c,*条件,对偶喷泉定理

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Abstract:

利用变分法,在n维空间有界区域Ω上,研究了一类含有Sobolev-Hardy临界指数与Hardy项的奇异椭圆方程Neumann问题弱解的存在性和多重性.在f(x,t)满足非二次条件的情况下,运用对偶喷泉定理与拉直边界的方法,证明了存在λ*>0使得当λ∈(0,λ*)时,该问题存在无穷多个具有负能量的弱解{u_k}被包含于W^{1,2}(Ω)并且当k→∞时,J(u_k)→0.

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