Existence of solutions for elliptic equations with critical Sobolev-Hardy exponents

摘要

Let Omega subset of R-N be a smooth bounded domain such that 0 is an element of Omega, N less than or equal to 3, 0 greater than or equal to 3, 0 less than or equal to s < 2, 2* (s) := 2(N-s)/(N-2),2 < r < 2* := 2N/(N-2). Via the variational methods, We prove the existence of sign-changing solutions for the singular critical problem -Deltau - muu/x(2) = u(2* (s) - 2)/xs u + lambdau(r - 2)u with Dirichlet boundary condition on Omega for suitable positive parameters lambda and mu. (C) 2003 Elsevier Ltd. All rights reserved.