Sentence examples for many solutions which from inspiring English sources

Eq. (11) has uncountably many solutions which are bounded by the functions u, v.

We use local sparsity model as prior to regularize this problem that has infinite many solutions which satisfy (37).

Since there are infinitely many solutions which satisfy (26) with the choice of m taken with (27), the proof is now complete.

If g is a transcendental meromorphic function, by Corollary D, then (g^{n}g^{ k)}-a= 0) has infinitely many solutions, which is a contradiction.

If K is a radially symmetric function such that (K_(0)=K_ infty)=0), then problem ((mathscr{P}^{K}_{0})) possesses infinitely many solutions which are radially symmetric.

As much as we know, in the literature there is no result for the existence of uncountably many solutions which are bounded below and above by positive functions.

Since the interval [ K 1, K 2 ] contains uncountably many constants, then Eq. (1) has uncountably many positive solutions which are bounded by the functions u ( t ), v ( t ).

We find the sufficient condition for nonexistence of entire large positive solutions and existence of infinitely many entire solutions, which are large or bounded.

The article deals with the existence of uncountably many positive solutions which are bounded below and above by positive functions for the first-order nonlinear neutral differential equations.

So any positive solution of (16) is nondegenerate and asymptotically stable, and (operatorname{index}_{tilde{P}}(B,w)= -1)^{0}= -1 which implies that (16) has at most finitely many positive solutions, which we denote by ({w_{i},1leq ileq l}).

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