Uniqueness conjecture for positive solutions of indefinite $\phi$-Laplacian boundary value problems

Let $a\in L^{\infty}(0,T)$ satisfy the assumptions in (hp-a), and let $\gamma\in\mathbb{R}\setminus\{-1,0,1\}$. Consider the Neumann and periodic boundary value problems associated with equations (u” ) and (p), respectively. Uniqueness conjecture. Each of these boundary value problems has at most one positive solution. The conjecture concerns uniqueness of positive solutions for indefinite $\phi$-Laplacian-type equations and extends the uniqueness results established under more restrictive parameter or weight assumptions; its validity for all allowed $\gamma$ remains open in the supplied source.