Sentence examples for exists sufficiently small from inspiring English sources

There exists sufficiently small constant such that for any,.

then we can easily know that there exists sufficiently small such that (4.21).

Then, it follows from the assumption that there exists sufficiently small, such that.

Then there exists sufficiently small (r>0) such that (psi varsigma r geq r).

Then there exists sufficiently small λ* > 0 such that the problem (1.1) has at least one positive solution for any λ ∈ (0, λ*).

(3.16) From (3.12) and (lim_{tau rightarrow 0}lambda_{tau }= widetilde{lambda }_{1}), we know there exists sufficiently small (tau in (0,1)).

Then (3.30) implies that, for any given (lambda>0), there exist sufficiently small (s_{0lambda}in 0,1)) and (varepsilon>0) such that mathcal{J}(s_{0lambda}u)< -varepsilon,quad forall uin K_{m}.

Suppose that is real analytic on Let Suppose that satisfies (1.5) and then there exists a sufficiently small such that if there exists, such that the Hamiltonian system (1.12) at has an invariant torus with as its frequency.

Consider the parameterized Hamiltonian system (2.1), which is real analytic on Then there exists a sufficiently small such that if there exists a Cantor-like family of analytic curves (2.5).

Since for there exists a sufficiently small such that (3.20).

If and, there exists an sufficiently small, such that (4.6).