I'm studying a paper and in the introduction appears the following: It is well known that existence of critical points and solvability of Euler-Lagrange equations are related, and there is and extensive literature about critical points which are minimizers, specially for functionals defined on the Sobolev space $W_{0}^{1,p}(\Omega),\; p>1,$ by $$J(u)=\int_{\Omega}\mathcal{F}(x,u,Du) dx,$$ where $\Omega$ is bounded, open subset of $\mathbb{R}^N.$

**DOUBT:** However, I'm struggling to find this extensive literature, and I also would like to find definition and properties of Euler-Lagrange equations.

Thanks in advance. I appreciate any help.