Sentence examples for solution given by from inspiring English sources

The solution given by John Allen Paulos to Charles Dodgson's (Lewis Carroll's) classic puzzle about mixing water and brandy (mentioned in Paulos's review of "Lewis Carroll in Numberland," Feb. 1) may be mathematically correct, but it is wrong in practice.

has a unique solution given by (2.6).

has a unique mild solution given by (2.8).

Let f ϵ be the regularized solution given by (20).

Then problem (2.6) has a unique solution given by (2.8).

Theorem 3.2 Let f N δ be the regularized solution given by (3.11), and let f be the exact solution given by (3.7).

Corollary 3.3 Let u N δ be the regularized solution given by (3.12), and let u be the exact solution given by (3.8).

System (3.1) has a unique -periodic -mild solution given by (3.5) and (3.6).

Then by a direct computation, it follows that the solution given by (2.3) satisfies (2.2).

The periodic boundary value problem (3.1)–(3.4) has a unique solution given by (3.32).

Then for any and, the linear PBVP(2.5) has a unique mild solution given by (2.6).