We study classes of two-point boundary value problems of the form: ⎧ ⎨⎪ ⎪⎩-(& phi;(u'))' = & lambda;h(t)f (u) ; (0, 1) u(0) = 0 u'(1) + c(u(1))u(1) = 0, where & phi;(s) = isip-2s for p > 1, h E C1((0, 1], (0, oo)) is decreasing, c E C([0, oo), (0, oo)) is non-decreasing and bounded, and f E C1((0, oo), R) is increasing on [L, oo) for some L > 0, has infinite semipositone structure at 0, and growth at oo like uq for q E (0,p -1). For classes of such h and f, we establish the uniqueness of positive solutions for & lambda; ⠅1. & COPY; 2023 Elsevier Inc. All rights reserved.