On ordinary differential equations with quasimonotone increasing right-hand side
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We prove that the initial value problem x ' (t) = f (t,x (t)), \( t \in [0,T] \), x (0) = x 0, is uniquely solvable in certain ordered Banach spaces if, f is quasimonotone increasing with respect to x, and if f is satisfying a one-sided Lipschitz condition with respect to the order-inducing cone.
KeywordsDifferential Equation Banach Space Ordinary Differential Equation Lipschitz Condition Order Banach Space
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