Sentence examples for maximal principle and from inspiring English sources

We obtain the following criteria according to the maximal principle and they are a sufficient condition for convergence to an accurate solution.

By means of a new maximal principle and new definitions of lower and upper solutions, the monotone iterative technique will be used in our investigation of the problem (1.1).

By calculating using general ordinary differential equation theory and maximal principle, we obtain that the radial function ϕ 0 ( x ) = q ( h 1 − h 2 ) ρ N − 2 ( ρ + 1 ) N − 2 ( ρ + 1 ) N − 2 − ρ N − 2 | x | N − 2 + [ q h 1 − ω − q ( h 1 − h 2 ) ( ρ + 1 ) N − 2 ( ρ + 1 ) N − 2 − ρ N − 2 ]. is the unique solution of equation (27).

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo- as well as positive solutions for fourth-order singular -Laplacian differential equations with integral boundary conditions.

A necessary and sufficient condition for the existence of smooth positive solutions is given by constructing lower and upper solutions and with the maximal principle.

Then Balakrishnan proved a maximal principle for the optimal control and which can imply the bang bang property (see [4]), Friedman discussed the time optimal control problem on Banach spaces (see [5]), Fattorini proved that the maximal principle in 1974 for some special Banach spaces.

The grid spacings of difference scheme are obtained by analyzing numerical stability and convergence based on the maximal principle.

By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle.

Lemma 1.3 (maximal principle).

end{cases} (2.16) It follows from the maximal principle that (u^_{k}< r).

subject to the state Eq. (1.2) by using Pontryagin's maximal principle.