Positive solutions for a higher order p-Laplacian boundary value problem with even derivatives

In this work, we study the existence and multiplicity of positive solutions for the higher order p-Laplacian boundary value problem with even derivatives { (φp((−1)x)) = f(t, x,−x′′, . . . , (−1)n−2x(2n−4)), αx(2i)(0)− βx(2i+1)(0) = 0, γx(2i)(1) + δx(2i+1)(1) = 0, where t ∈ [0, 1], n ≥ 2, i = 0, 1, . . . , n, α, β, γ, δ ≥ 0 with ρ := αγ + αδ + βγ > 0 and f ∈ C([0, 1] × Rn−1 + ,R+) (R+ := [0,∞)). By virtue of some properties of concave functions and Jensen’s integral inequality, we adopt fixed point index theory to establish our main results. Moreover, our nonlinear term f is allowed to grow superlinear and sublinear.