Mathematics · Calculus of Variations
Consider the variational problem (P): J(y(x)) = ∫01 [(y')2 − y|y|y' + xy] dx, subject to boundary conditions y(0) = 0 and y(1) = 0. Which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(P) has infinitely many stationary functions (extremals).
- 2(P) has a unique stationary function (extremal) y that is not identically equal to 0.✓
- 3y ≡ 0 is the only stationary function (extremal) for (P).
- 4(P) has no stationary function (extremal).
Correct answer
(P) has a unique stationary function (extremal) y that is not identically equal to 0.
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