Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Euler-lagrange Equation
Let \(X=\left\{u \in C^1[0,1] \mid u(0)=u(1)=0\right\}\) and define J : X → ℝ by \(J(u)=\int_0^1 e^{-u^{\prime}(x)^2} d x\) Then
1
J does not attain its infimum
2
J attains its infimum at a unique u ∈ X
3
J attains its infimum at exactly two elements u ∈ X
4
J attains its infimum at infinitely many u ∈ X
5
Question Not Attempted