NONLINEAR EIGENVALUE PROBLEM FOR P-LAPLACIAN IN R(N)

The nonlinear eigenvalue problem for p-laplacian -div (a(x) \del u\(p-2) del u) = lambda f(x, u), x is an element of R(N); lambda > 0, u > 0, in R(N), lim u = 0, \x\-->infinity is considered. We assume 1 < p < N and that the function f is of subcritical growth with respect to the variable u. The existence and C-1,C-alpha-regularity of the weak solution is proved.