Sentence examples for bounded positive solution of from inspiring English sources

(4.4). is a bounded positive solution of (1.1).

In particular, we find that any bounded positive solution of the above equation must be constant under some suitable assumptions.

end{aligned} which shows that T is a contraction mapping on A and therefore there exists a unique solution, obviously a bounded positive solution of (1) (mathbf{x}in A), such that (Tmathbf{x}=mathbf{x}).

Assume that u is a bounded positive solution of (1.6) and (1.7) with J = ( 0, ∞ ) such that for some sequence t n → ∞, lim inf n → ∞ u ( x, t n ) > 0 ( x ∈ Ω ).

end{aligned} This implies with the sup norm that |Tx_{1}-Tx_{2}|< |x_{1}-x_{2}|, which shows that T is a contraction mapping on A and therefore there exists a unique solution, obviously a bounded positive solution of (1) (xin A), such that (Tx=x).

Here, w is the unique bounded positive solution of (48 ).

Thus the set of bounded positive solutions of Eq. (1.11) in (A(N,M)) is uncountable.

In order to prove that the set of bounded positive solutions of Eq. (1) is uncountable, it is sufficient to verify that x ≠ y.

When J = ( 0, ∞ ), Hess and Poláčik [25] first studied the asymptotic symmetry results for classical, bounded, positive solutions of the problem u t − Δ u = f ( t, u ), ( x, t ) ∈ Ω × J, (1.6).

In the past thirty years there has been much research activity concerning the oscillation, nonoscillation, asymptotic behavior and existence of solutions, nonoscillatory solutions and bounded positive solutions for various kinds of neutral delay difference equations, see, for example, [1 25] and the references therein.

end{aligned} Using Krasnoselskii's fixed point theorem, we obtain the existence of uncountably many bounded positive solutions to the considered problem.