On a Theorem of Mierczyński
Tom 76 / 1998
Colloquium Mathematicum 76 (1998), 19-29
DOI: 10.4064/cm-76-1-19-29
Streszczenie
We prove that the initial value problem x'(t) = f(t,x(t)), $x(0) = x_1$ is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.
