Multiple positive solutions for Dirichlet problems involving concave and convex nonlinearities

In this paper, we study the multiplicity of positive solutions for the following Dirichlet problems involving concave and convex nonlinearities {−Δu+u=λf(x)|u|q−2u+h(x)|u|p−2uin A;u∈H01(A), where 1≤q<20,A=Θ×R is an infinite strip in RNRN, ΘΘ is a bounded domain in RN−1RN−1 and f(x),h(x)f(x),h(x) satisfy suitable conditions.