Unique solution of periodic boundary value problems (Q1178672)

First order periodic boundary value problems are studied by use of upper and lower solutions. In two theorems, the author asserts unique solvability of the given problem in the function strip between upper and lower solution, provided that these exist and satisfy the ``right'' inequality, and that the nonlinearity satisfies a one-sided Lipschitz condition. The (identical) proofs of the two theorems contain a severe mistake: The operator \(B\) considered there is (in general) clearly not decreasing, and its image consists of more than a single function. Nevertheless, the results seem to be correct, as could be proved by monotone iteration techniques.