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I have got this problem in exam where I have to to check for strong maxima (or minima) or weak maxima(or minima) of the functional given by

$\int_{0}^{1} (1+x)(y^')^2 dx ~~~~~ y(0) = 0, ~~ y(1) = 1$.

I have studied that necessary condition such that the function $y(x)$ minimizes or maximizes the integral $ I =\int_{0}^{1} F(x,y,y^') dx $ for a given function $F$ and for given values of $y(x_1)$ and $y(x_2)$ is given by the Euler-Lagrange equation. But I haven't studied about strong or weak extrema. I tried to study from wiki link, but still not able to understand. I need help with this.

Edit: I welcome references or online study material related with this topic.

Thank you very much

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