I know that such kind of functions are completely monotone functions. but its successive derivative changes sign. and you pointed out that this does not change sign, how? the function is positive and its derivative is negative and the second derivative will agian be positive.
changes sign at every point on the domain.
if we have a function f(x)=exp(-a*x) then f'(x)=-a*exp(-a*x),
f''(x)=a^2*exp(-a*x) and so on...
similarly if we have f(x)=(a^2+x)^(-1/2) then f'(x)=(-1/2)*(a^2+x)^(-3/2)
and f''(x)(-1/2)*(-3/2)*(a^2+x)^(-5/2) and so on...
i think that if we have...
Homework Statement
This is ralated to completely monotone functions. if a function and its successive derivative changes sign then what does this mean?
Homework Equations
The Attempt at a Solution
I need guidance regarding PDE.
If u have a nonlinear PDE as
Ut+Us+a*U*Us*b*Usss=0
where U is function of (s,t) and a,b are constants.
by introducing new variable x=s-t we will get
Ut+a*U*Ux+b*Uxxx=0
Ut means partial derivative w.r.t time
Us means partial derivative w.r.t s.
How can we...