貓朋
Lv 5
貓朋 asked in 科學及數學數學 · 1 decade ago

Maximum Principle (1)

Let φ∈C^2[a,b] such that

-φ''(x) ≧0 , a≦x≦b,

φ(a) ≧0

φ(b) ≧0

then φ(x) ≧0 , a≦x≦b

Update:

-φ''(x) >= 0 , a =< x =< b,

φ(a) >= 0

φ(b) >= 0

then φ(x) >= 0 , a =< x =< b

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