Sentence examples for monotone condition from inspiring English sources
Lavi and Swamy first use the cycle monotone condition and design a 3-approximation truthful mechanism for a two value variant in [R.
Moreover, if x 0 ∈ L p ( Ω ; R d ), p ≥ 2, then E | x ( t ) | p < ∞ under the monotone condition.
It is not hard to see that the same remains true if the monotone condition on the modulus is replaced by lower semicontinuity from the right.
Now, we are ready to present our fixed point theorem, in which no monotone condition is assumed on the nonlinear operator.
This technique combines the idea of method of upper and lower solutions with appropriate monotone conditions.
Under some monotone conditions and noncompactness measure conditions of the nonlinearity, some existence and uniqueness results are obtained.
where L i, i = 0, …, n − 1, are continuous functions without assuming monotone conditions or another type of variation.
Further, under wide monotone conditions and the noncompactness measure conditions, we obtain the existence of extremal solutions and a unique mild solution between lower and upper solutions.
Under wide monotone conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique mild solution between lower and upper solutions.
