Journal of East China Normal University(Natural Sc ›› 2011, Vol. 2011 ›› Issue (5): 79-87.

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

CHEN Zi-gao   

  1. Department of Mathematics and Information Science, North China, University of Water Resources and Electric Power, Zhengzhou 450011, China
  • Received:2011-03-01 Revised:2011-06-01 Online:2011-09-25 Published:2011-11-22

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 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→∞.

Key words: Neumann problem, critical Sobolev-Hardy exponent, (PS)_c^* condition, dual fountain theorem

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