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

Abstract

The paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the φ-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 ∈ ]−∞, (1 − 2p)/(p − 1)] ∪ ]p − 1, +∞[.