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- W1628615118 abstract "We consider the differential equation u′(t) = F(t, u(t)), where X is a real Banach space, I is a nonempty and open interval, K a nonempty and locally closed set in X and F : I × K → X is a Lipschitz quasi‐compact Carathéodory function. We prove that a necessary and sufficient condition in order that for each (τ, ξ) ∈ I × K there exists T > τ such that the equation above has at least one solution u : [τ, T] → K is the Carathéodory Tangency Condition: (CTC) there exists a negligible subset F of I such that, for each (τ, ξ) in (I F) × K, lim infs↓01sd(ξ + sF(τ, ξ); K) = 0. Some applications to the existence problem for two classes of semilinear partial differential equations are also included." @default.
- W1628615118 created "2016-06-24" @default.
- W1628615118 creator A5054083146 @default.
- W1628615118 date "2006-01-01" @default.
- W1628615118 modified "2023-10-17" @default.
- W1628615118 title "A viability result for a class of ordinary differential equations in Banach spaces" @default.
- W1628615118 doi "https://doi.org/10.1063/1.2205044" @default.
- W1628615118 hasPublicationYear "2006" @default.
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