Sentence examples for establish the comparison from inspiring English sources

In Section 2, we establish the comparison principle.

We establish the comparison principle under natural and mild conditions.

In Section 2, we shall establish the comparison principle and local existence theorem for problem (1.1).

In Section 2, we establish the comparison principle and the local existence.

Then we establish the comparison principle and discuss the uniqueness and the uniform bound.

In Section 2, we establish the comparison lemmas to prove the uniqueness of the positive solution to (1.9) and the identification of the half-relaxed limits.

In this section, we propose a new S-type eigenvalue set for tensors and establish the comparisons between this new set with those in Lemmas 1.1-1.4 1.1-1.4

We remark that (Pham and Zhang 2014) established the comparison principle for viscosity solutions of this PPDE in the sense of Definition 2.2.

The more recent paper Ren et al. (2016b) established the comparison for fully nonlinear degenerate PPDEs, by introducing a regularization operator which can be viewed as the counterpart of the sup-convolution in the PDE literature.

and establish the norm comparison theorem for and.

Inspired by the ideas in [5, 6], we shall establish the following comparison result.