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These are replies submitted by Zeineb


in this case : y=0 and 3<=x<=4, we get g =0<=0  ( this case is true)

I  want to show that max{g(x,y)} <=0 less or equal zero.


Thank you

this can be proved by hand, its enough to use that 1-y/1+y always less than one. after that we obtain a function which depends only on x and simple derivative give us the critical point. 



Thank you for your time to see my question.

The solution proposed by maple satify all conditions maybe its the unique solution


My vector is [u[1, 0], u[2, 0], u[3, 0], u[1, 1], u[2, 1], u[3, 1], u[1, 2], u[2, 2], u[3, 2], u[1, 3], u[2, 3], u[3, 3]]
the quanties



u[0, 0]=  u[0, 1]= u[0, 2]= u[0, 3]=100

so all these parameters are fixed.



the quantities f[1, 0], f[1, 1], f[1, 2], f[1, 3], f[2, 0], f[2, 1], f[2, 2], f[2, 3], f[3, 0], f[3, 1], f[3, 2], f[3, 3]   are constant , we can drop them from the sytem if you want, my goal is obtain the matrix whose entries are coefficient of u[i,j]



Thank your for your remarks

maybe empty solution because f is discontinous function


Please find the modified version of the code but how can we deduce the general form of u[n]


@Preben Alsholm 

Thank you for your remark. We can fix N=10 for example


thank you for your answer.

can we obtain a general solution without specify the vectors v[i] and for general n

@Axel Vogt 

I compare


  I see there is a difference between them



Thank you for your help

I use maple 18



@Carl Love 

The ODE is defined for all x in [o,1] except 1/2

The piecewise function is differentiable ( or piecewise differentiable) and it is derivative equal zero ( defined as piecewise function) so it is a solution


There are three solutions:

1) C1=C2

2) C1=-C2

3) C1 and C2 are orthogonal

the three cases give D1=D2


Thank you for the code.

We get that the vectors  C1  and  C2  either:
1) coincide or 
2) differ from each other by turning by an angle multiple of  90  degrees

And a  third case,

differ from each other by turning by an angle multiple of  180  degrees

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