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For the sustainable development of urban rail transit, an operational subsidy is a way to increase operators' profits and can balance profits among government, operators, and passengers.
Nevertheless, this solution would largely increase operators' expenditures.
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However, this solution would increase operator costs.
New functionalities improve work quality and increase operator comfort.
The ECH control system software will be upgraded for increased scalability and to increase operator productivity.
Existence theorems of fixed points for multivalued increasing operators in partially ordered spaces are presented.
Nguyen and Nguyen [17] investigated the fixed points for multi-valued increasing operators and then in [18], a fixed point theorem for a multi-valued increasing operator was established and applied to a discontinuous elliptic equation.
In [9 11], the authors obtained the minimal and maximal positive solutions by using a fixed point theorem of increasing operators.
But in most well-known documents, it is assumed generally that increasing operators possess stronger continuity and compactness.
It is a common knowledge that fixed point theorems on increasing operators are used widely in nonlinear differential equations and other fields in mathematics ([1 7]).
Motivated by the works mentioned above, in this article we study the differential equations (1.1) by using the fixed point theorem for increasing operators on the order intervals.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com