MULTIPLE SOLUTIONS FOR A CLASS OF DEGENERATE NONLOCAL PROBLEMS INVOLVING SUBLINEAR NONLINEARITIES

In this article, we use the three critical points theorem by G. Bonanno [3] in order to investigate the multiplicity of solutions for nonlocal degenerate problems of the form { -M(integral Omega vertical bar x vertical bar (-ap)vertical bar del u vertical bar(p) dx) div ( vertical bar x vertical bar(-ap)vertical bar del u vertical bar(p-2 del)u) =lambda vertical bar x vertical bar(-p(a+1)+c) f(u) in Omega, u=0 on partial derivative Omega, where Omega subset of R-N (N >= 3) is a smooth bounded domain, 0 is an element of Omega, 0 <= a< N-p/p , 1 < p < N, c > 0, and M : R+-> R is a continuous function that may be degenerate at zero, f : R -> R is continuous and sublinear at infinity.