This phenomenon also causes a corollary problem for fund managers.
Therefore, by Corollary 3.3, problem (4.1) has at least two positive solutions, satisfying.
Then as corollaries, the problems of determining the weak detectability and weak periodic detectability of nondeterministic DESs are also PSPACE-hard (hence PSPACE-complete).
Therefore, as a consequence of Corollary 9, problem (27) does not admit a global nontrivial solution when (c_{0}geq0).
Corollary 2.3 Problem (2.5) has a unique solution if and only if u ˜ ( t 0 ) ≠ 0. Proof Considering Lemma 2.2 III), u ˜ and v ˜, defined as in (2.8) and (2.9), respectively, satisfy the hypothesis of Theorem 2.1, (h1), therefore a solution exists.
By Corollary 2.6, the problem of finding the solutions of the problem (3 - 5) is reduced to finding the solutions of the operator equation N ( u ) = u.
So, by this corollary, the considered problem has solutions.
Thus, by a simple computation, we show by Corollary 2 that problem (9) has a solution.
Thus, by Corollary 3.3, the problem (4.4) with (4.5) has at least one solution on ([1,e]).
Therefore, by Corollary 3.4, the problem (4.4) with (4.6) has at least one solution on ([1,e]).
