MULTIPLE POSITIVE SOLUTIONS FOR SINGULAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND SIGN-CHANGING POTENTIAL

In this paper, we are interested in considering the following singular elliptic problem with concaveconvex nonlinearities {-Delta u - mu/vertical bar x vertical bar(2)u = f(x)vertical bar u vertical bar(p-2)u+g(x)vertical bar u vertical bar(q-2)u, in Omega\{0}, u=0, on partial derivative Omega, where Omega subset of R-N(N >= 3) is a smooth bounded domain with 0 is an element of Omega, 0 < mu < (mu) over bar = (N-2)(2)/4, 1 < q < 2 < p < 2* and 2*=2N/N-2 is the Sobolev critical exponent, the coefficient functions f, g may change sign on Omega. By the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.