带临界指数的奇异椭圆方程Neumann问题多重解的存在性

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.

Existence of multiple solutions for singular elliptic equations involving critical exponents with Neumann boundary condition

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 Ω 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 λ*>0 such that for any λ∈(0,λ*), this problem has a sequence of solutions {u_k} W^{1,2}(Ω) such that J(u_k)<0 and J(u_k)→0 as k→∞.