Sentence examples for some maximum principles from inspiring English sources

In this section, we prove some maximum principles.

From these inequalities, we derive, using Hopf's maximum principles, some maximum principles for the appropriate combinations of and, and we list a few examples of problems to which these maximum principles may be applied.

We introduce a new definition of lower and upper solutions with integral jump conditions and prove some new maximum principles.

By introducing some auxiliary functions and using maximum principles, they established some conditions on nonlinearities to guarantee the existence of blow-up solution or global solution.

By constructing some auxiliary functions and using maximum principles, the sufficient conditions were obtained there for the existence of global and blow-up solutions.

Our research relies mainly on constructing some auxiliary functions and using the parabolic maximum principles and the differential inequality technique.

We technically use maximum principles to deal with problem (1.1).

See [22, 24]) for a general study of maximum principles.

Although in many cases, speaking about maximum principles, authors mean quite different definitions of maximum principles (such as e.g., corresponding inequalities, boundedness of solutions and maximum boundaries principles), there exists a deep internal connection between these definitions.

2, we will present our results on maximum principles for elliptic Waldenfels operators.

In this paper, we technically use maximum principles to deal with problem (1.1).