In this paper, we prove the existence of eigenvalues for the problem where φp(s)=sp−2s, p>1, λ is a real parameter and the indefinite weight h is a nonnegative measurable function on (0,1) which may be singular at 0 and/or 1, and h 0 on any compact subinterval in (0,1). We derive similar properties of eigenvalues as known in linear case (p=2) or continuous case (h C[0,1]) if h satisfies when 1
0 for s≠0, f is odd and f(s)/φp(s) is bounded above as s→0.
