Sentence examples for mild solutions between from inspiring English sources

Then by Corollary 3.2, the system (4.1) has the minimal and maximal mild solutions between 0 and w. □.

Theorem 4.2 If (a - d) a - daresatisfieden thensysthe (4.1) hasystemminimal and maximal mild solutions between 0 and w.

Then, the Cauchy problem (1.1) has the minimal and maximal mild solutions between v0and whichhicancan be obtained by a monotone iterative procedure starting from v0and w0, respectively.

If the conditions (H1) and (H2) are satisfied, then problem (1.1) has minimal and maximal mild solutions between (y_{0}) and (x_{0}), which can be obtained by a monotone iterative procedure starting from (y_{0}) and (x_{0}), respectively.

Then problem (1.1) has minimal and maximal mild solutions between ([y_{0},x_{0}]), which can be obtained by a monotone iterative procedure starting from (y_{0}) and (x_{0}), respectively.

Finally, we show that problem (1.1) has minimal and maximal mild solutions between ([y_{0},x_{0}]), which can be obtained by a monotone iterative procedure starting from (y_{0}) and (x_{0}), respectively.

Therefore, the system (2) has at least one mild solution between (underline{u}) and u̅.

Under wide monotone conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique mild solution between lower and upper solutions.

Further, under wide monotone conditions and the noncompactness measure conditions, we obtain the existence of extremal solutions and a unique mild solution between lower and upper solutions.

Then, the Cauchy problem (1.1) has the unique mild solution between v0and whichhicancan be obtained by a monotone iterative procedure starting from v0or w0.

If the conditions (H1), (H2), and (H4) hold, then problem (1.1) has a unique mild solution between (y_{0}) and (x_{0}), which can be obtained by a monotone iterative procedure starting from (y_{0}) or (x_{0}).