The existence question in the calculus of variations: a density result

Cellina, Arrigo; Mariconda, Carlo

doi:10.1090/S0002-9939-1994-1174488-2

The existence question in the calculus of variations: a density result
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by Arrigo Cellina and Carlo Mariconda PDF

Proc. Amer. Math. Soc. 120 (1994), 1145-1150 Request permission

Abstract:

We show the existence of a dense subset $\mathcal {D}$ of $\mathcal {C}(\mathbb {R})$ such that, for $g$ in it, the problem \[ {\text {minimum}}\;\int _0^T {g(x(t))dt + \int _0^T {h(x’(t))dt,\;x(0) = a,\;x(T) = b} } \] admits a solution for every lower semicontinuous $h$ satisfying growth conditions

References

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Alcune osservazioni sull’esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessitá

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