一类具有弱增长性的Bolza问题

On a Class of Nonconvex Variational Problems with Slow Growth

我们考虑最小值问题(P)min{ab∫f(t,u′(t))dt+l(u(a),u(b));u∈AC([a,b],Rn)},其中f:[a,b]×Rn→R∪{+∞}是正规被积函数,l:Rn×Rn→R∪{+∞}下半连续,AC([a,b],Rn)表示从[a,b]到Rn的绝对连续函数空间。我们将证明最小化算子存在的充分条件。

In this paper we Consider the minimization problem （P）min{ab∫f（t,u′（t））dt＋l（u（a）,u（b））;u∈AC（[a,b],Rn）},Wheref：[a,b]×Rn→R∪{＋∞} is a normal integrand,l：Rn×Rn→R∪{＋∞} is a lower semicontinuous function, and AC（[a, b ],R^n ）denotes the space of absolutely continuous functions from [ a,b ] to R^n .We prove sufficient condition for the existence of minimizers.