The Banach contraction principle [1] may be considered as one of most powerful tools for establishing existence and uniqueness of solutions for various non linear problems.
These results give sufficient conditions for establishing the existence (and uniqueness) of solution of certain integral operators, see [50 52].
First, we give the concept of 0-diagonally convex which is useful for establishing the existence theorem for the problem ( P ).
J Time Ser Anal 2013; 34(1): 83–95 and the ARDL bounds testing approach to cointegration for establishing the existence of long-run relationship in presence of structural breaks.
The method of this paper is a unified method for establishing the existence of positive solutions for a large number of nonlinear differential equations with coupled boundary conditions.
In fact, the proof of the convergence of the Carathéodory approximation represents an alternative to the procedure for establishing the existence and uniqueness of the solution to delay DPSDEs.
Given the existence of established inhibitors for HDACs and the elucidation of a selective TG2 inhibitor herein (ZDON), a head-to-head comparison of TSA or butyrate to ZDON, or a combination of two of these is in order.
In JWBG2 the existence of cycles in equilibrium above this line is not confirmed, while in JWBG1 their existence is established for (c<1), and their necessity is proved for (c>1) (Sect. 5.3).
Here, we only refer the reader to [2 4], wherein the global existence was established for (1), with the condition that the initial density needs to be bounded a way from zero.
The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato and Ponce (1988) [13].
