Calculus of variation

  • #1
581
10

Main Question or Discussion Point

If for some functional ##I##, ##\delta I=0## where ##\delta## is symbol for variation functional has extremum. For ##\delta^2 I>0## it is minimum, and for ##\delta^2 I<0## it is maximum. What if
##\delta I=\delta^2 I=0##. Then I must go with finding further variations. And if ##\delta^3I>0## is then that minimum? Or what?
 

Answers and Replies

  • #2
6,054
390
I suggest you ask the same question in a simpler situation: ordinary single-variable function.
 
  • #3
1,948
200
Use the first non-vanishing derivative. If it is an odd derivative, than you have and inflection point, otherwise it will be either a maximum or a minimum depending on its sign
 

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