Sentence examples for main existence and from inspiring English sources

The main existence and uniqueness result is stated and proved in Sect.

The next theorem is our main existence and comparison result for the BVP (6.1).

The main existence and convergence result of this article we can now state as follows.

In Section 3 we present the main existence and uniqueness results for the problem (1.1).

The main existence and localization result is applied to a partial integro-differential equation involving possible discontinuities in state variables.

Assume that L loc (a, b] is ordered a.e. pointwise, that Y is ordered pointwise, and that the functions p, f, c and d satisfy the following hypotheses: Our main existence and comparison result for the IVP (5.1) reads as follows.

The main existence results are Theorem 3.1 and Theorem 4.2.

Moreover, Luc et al. [19] established two main existence conditions for solutions of variational relation problems without convexity, and Pu and Yang [20 22] studied variational relation problems without the KKM property and on Hadamard manifolds.

The main existence results for problem (1.1 - 1.2 1.1 - 1.2ined in Section 3, are the examples illustrating the results obtainedon 3 are ginen in Section 4.

The main existence forms of Cr in groundwater are the oxidation states of Cr III) and Cr VI) (Barrera-Díaz et al. 2012).

2, we introduce some important notions about fractional difference operators and topological degree theory, while Sect. 3 contains our main existence results for Eq. (1.1).