Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition
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摘要: 利用变分法, 在n维空间有界区域上, 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*0使得当(0,*)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}()并且当k时, J(u_k)0.
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关键词:
- Neumann问题 /
- Sobolev-Hardy临界指数 /
- (PS)_c^*条件; 对偶喷泉定理
Abstract: By using variational methods, the existence and multiplicity of weak solutions for Neumann boundary problem for some singular elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms was studied on bounded domain included by R^N. If f(x,t) satisfies the non-quadratic condition, based on the dual fountain theorem and the means of straightening the boundary, we proved that there exists *0 such that for any (0,*), this problem has a sequence of solutions {u_k} W^{1,2}() such that J(u_k)0 and J(u_k)0 as k.-
Key words:
- Neumann problem /
- critical Sobolev-Hardy exponent /
- (PS)_c^* condition
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