One-sided Resonance for Quasilinear Problems with Asymmetric Nonlinearities

for two consecutive variational eigenvalues, λl < λl+1 of −∆p on W 0 (Ω), and some ε > 0 (see Section 2 for the definition of the variational spectrum). The special case where α+(x) = α−(x) ≡ λl and q = 1 was recently studied by Arcoya and Orsina [1], Bouchala and Drábek [3], and Drábek and Robinson [8] (see also Cuesta et al. [6] and Dancer and Perera [7]). In the present paper, we prove a single existence theorem for the general case that includes all their results and much more.