Sentence examples for boundary problems have received from inspiring English sources

In fact, free boundary problems have received considerable attention in many fields, such as tumor cure [11] and wound healing [12] in medicine, vapor infiltration of pyrolytic carbon in chemistry [13], and expansion of the area infected by the virus in epidemiology [14].

In view of the importance of anti-periodic boundary conditions in the mathematical modeling of a variety of physical processes [26 28], the study of anti-periodic boundary value problems has received considerable attention.

Since then, the existence of solutions for nonlinear multi-point boundary value problems has received much attention from some authors; see [2 6] for reference.

Since then, the existence of solutions for nonlocal boundary value problems has received a great deal of attention in the literature.

Multi-point boundary value problems have received considerable interest in the mathematical applications in different areas of science and engineering.

In the past few years, fractional-order boundary value problems have received much attention, and the subject has been developed in an extensive manner.

Because of the extensive applications in mechanics and engineering, nonlinear fourth-order two-point boundary value problems have received wide attentions (see [7 12] and references therein).

Kirchhoff-type problems have received much attention.

This problem has received a great attention.

This problem has received considerable attention recently.

The existence of solutions for systems of local and nonlocal boundary value problems (BVPs) has received increased attention by researchers; see, for example, the papers of Agarwal, O'Regan, and Wong [28 30], Henderson, Ntouyas, and Purnaras [31], Precup [32, 33] and the references therein.