Abstract

nor do we assume more smoothness than mere continuity of g(x, t) in t. In particular, no assumption concerning the modulus of continuity of g(x, t) in I is made. Castro and Lazer [l] studied (0.1) under the assumptions that A, < A’ 5 g(x, tyt I A” < A/+, and ag(x, t)/& is increasing in It I. Ambrosetti and Mancini [2] consider the situation when g(x, t) = &r + J-(x, r) with f(x, f) uniformly bounded. Thews [3) assumed (1J + h,(x, f))/f 5 g(x, t)/t 5 (&+it hz(x, t))/t where the hi are bounded and satisfy

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