2.3 Consider the system x' = f(t, x), x (to) = xo, to 0, where...

Transcribed Image Text:

2.3 Consider the system x' = f(t, x), x (to) = xo, to ≥ 0, where the function f : [0, ∞) x R" → R" is continuous in (t, x), locally Lipschitz in x and satisfies the condition (f(t, x), Px) ≤0, \t≥0, x ≤R", where P is a real, symmetric and positive definite n x n matrix. Prove that any right-saturated solution of the system is defined on the semi-axis [to, ∞). (2.110) 2.3 Consider the system x' = f(t, x), x (to) = xo, to ≥ 0, where the function f : [0, ∞) x R" → R" is continuous in (t, x), locally Lipschitz in x and satisfies the condition (f(t, x), Px) ≤0, \t≥0, x ≤R", where P is a real, symmetric and positive definite n x n matrix. Prove that any right-saturated solution of the system is defined on the semi-axis [to, ∞). (2.110)

Answer rating: 100% (QA)

Proof Let xt be a rightsaturated solution of the system To prove that xt is defined on the semiaxis ... View the full answer