We show the existence of a dense subset D of C(R) such that, for g in it, the problem minimum integral-T/0 g(x(t))dt + integral-T\0 h(x'(t))dt, x(0) = a, x(T) = b admits a solution for every lower semicontinuous h satisfying growth conditions
The Existence Question In the Calculus of Variations - A Density Result
MARICONDA, CARLO
1994
Abstract
We show the existence of a dense subset D of C(R) such that, for g in it, the problem minimum integral-T/0 g(x(t))dt + integral-T\0 h(x'(t))dt, x(0) = a, x(T) = b admits a solution for every lower semicontinuous h satisfying growth conditions
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