Nonoscillation Of Nonlinear Retarded Differential Equations
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.
We prove that the initial value problem x’(t) = f(t,x(t)), 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.
On an infinite-dimensional Hilbert space, we establish the existence of solutions for some evolution problems associated with time-dependent subdifferential operators whose perturbations are Carathéodory single-valued maps.