Uniqueness of positive solutions for boundary value problems associated with indefinite φ-Laplacian-type equations

This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the φ-Laplacian equation (φ(u'))' + a(t)g(u) = 0, where φ is a homeomorphism with φ(0) = 0, a(t) is a stepwise indefinite weight and g(u) is a continuous function. When dealing with the p-Laplacian differential operator φ(s) = |s|^{p-2}s with p > 1, and the nonlinear term g(u) = u^γ with γ ∈ ℝ, we prove the existence of a unique positive solution when γ ϵ ]-∞, (1-2p)/(p-1)] ∪ ]p-1,+∞[.