Sentence examples for mild solution when from inspiring English sources

In particular, the system (2.1) obviously has a trivial mild solution when.

Also, it is obvious that system (1) has a unique trivial mild solution when the initial value (varphi=0).

(4) Problem (1.1) has a unique mild solution when the conditions (H1), (H2), and (H4) in Section  3 are satisfied.  .

In Section 4, we prove that a mild solution, when it exists, is also a weak solution.

However, to the best of our knowledge, there is no work reported in literature on conditions under which the problem (4.1) has a unique asymptotically ω-periodic mild solution when the nonlinear perturbation is S-asymptotically or asymptotically ω-periodic in the Stepanov sense.

(2) Problem (1.1) has minimal and maximal mild solutions when the conditions (H1) ∼ (H3) in Section  3 are satisfied.

Using the techniques of approximate solutions and fixed point, existence results are obtained, for mild solutions, when the impulsive functions are only continuous and the nonlocal item is Lipschitz in the space of piecewise continuous functions, is not Lipschitz and not compact, is continuous in the space of Bochner integrable functions, respectively.

This allows us to apply Horn's fixed-point theorem to prove the existence of -periodic PC-mild solutions when PC-mild solutions are ultimate bounded.

However, one cannot ensure the unique existence of almost automorphic mild solution to (2.26) when (2.32).

In particular, the uniqueness result of mild solution is established when f satisfies the condition close to Nagumo-type condition.

In particular, the uniqueness result for a mild solution is obtained when f satisfies a condition weaker than Lipschitz condition.