The paper studies the existence of multiple solutions to the following p-Laplacian type elliptic problem (p > 1):

where Ω is a bounded domain in ℝN(N [ges ] 1) with smooth boundary ∂Ω, and f(x, u) goes asymptotically in u to [mid ]u[mid ]p−2u at infinity. It is well known that this kind of nonlinear term creates some difficulties in the application of the mountain pass theorem because of the lack of an Ambrosetti–Rabinowitz type superlinear condition on f(x, u). An improved mountain pass theorem is used to prove that the above problem possesses multiple solutions under some natural conditions on f(x, u), and some known results are generalized.