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Now note that The maximum principle gives.
Then the strong maximum principle gives (u-u_{0}equivtheta).
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On the other hand indirect methods are based on the Pontryagin Maximum Principle which gives a set of necessary conditions for a local minimum.
Applying the maximum principle on gives (2.8).
Finally, a convolution argument and the maximum principle plainly give (B.4).
The goal of this section is to get a priori upper and lower positive bounds for positive solutions of (3) by using the maximum principle and give some important lemmas.
Soon enough, principle gives way to pragmatism.
By the strong maximum principle, we have (u_{lambda}>0).
The Maximum Principle shows immediately that if a given Dirichlet problem has a solution, the solution is unique.
We now formulate a discrete maximum principle for the difference operator and give an estimate of the solution to (2.4).
Necessary conditions for optimality for problem P1 are given by the Pontryagin maximum principle.
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