Sentence examples for under a weak condition from inspiring English sources

Recently, Chen and Li contributed their interests on Thompson's conjecture under a weak condition.

We found, however, that under a weak condition, the formation of long-term auditory fear memory but not short-term memory was impaired by the ablation of striatal neurons.

Mao [10] provided an existence and uniqueness result under a weaker condition than the Lipschitz one.

Proposition 2 establishes that X is asymptotically stable under a weaker condition.

Next, we analyze the superlinear convergence rate of the iterative sequence under a weaker condition.

Later on, Spanne type results were obtained by Guliyev et al. [17] under a weaker condition.

In the present paper, we also use the three theorems in [10] and the linking technique to give the existence of at least one nontrivial solution for the biharmonic problem (1.1) under a weaker condition.

If and then from Kronecker-Capelli's theorem, see, for instance, [11, 15], there exist infinitely many solutions of the incremental controller gains which make so that the closed-loop stability is guaranteed under with On the other hand, Corollary 3.3 allows obtaining a subsequent direct result under a weaker Condition 2 of Theorem 3.2.

Using the formula (1.7) and the assumption, we find that T 1 ≤ ( A − B ) | t | ( 1 + | B | ) ( Γ ( c − | a | − | b | ) Γ ( c ) Γ ( c − | a | ) Γ ( c − | b | ) − 1 ) ≤ ( A − B ) | t |, which implies that the operator I a, b ; c f maps R t ( A, B ) into R t ( A, B ). If, in the proof of Theorem 3.2, we take b = a ¯, then we have the following theorem under a weaker condition on the parameter c. □.

So, Theorem 3.4 actually holds under such a weaker condition.

Next, we further give an existence result for the fractional differential inclusion (1.1 - 1.2 1.1 - 1.2relatively weak condition of F when g is not underrmly bounded.