Necessary and sufficient conditions for one-dimensional variational problems with applications to elasticity

Pavol Quittner

This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $\Phi (u)={\int }_a^{b}f(x,u(x),u^{\prime }(x))dx$, where $u\in C^1([a,b],{\mathbb{R}}^N)$.…