Abstract
A type of non-Newtonian filtration equations with variable delay is considered. Using a new approach which was established by Ge and Ren in (Nonlinear Anal. 58:477–488, 2004), we obtain the existence of periodic wave solutions for the non-Newtonian filtration equations. The methods of the present paper are markedly different from the existing ones.
Highlights
1 Introduction This paper is devoted to studying the periodic wave solutions problem for a type of nonNewtonian filtration equation with variable delay as follows:
In 1967, Ladyzhenskaja [2] studied Eq (1.2) for the description of incompressible fluids and solvability in the large boundary value of them, which is the first work for Eq (1.2)
As far as we know, the existence of periodic wave solutions for functional differential equations was obtained by the use of an extension of coincidence degree theory
Summary
This paper is devoted to studying the periodic wave solutions problem for a type of nonNewtonian filtration equation with variable delay as follows:. (2021) 2021:16 obtained the existence of solitary wave and periodic wave solutions for the above equation by using the extension of Mawhin’s continuation theorem. As far as we know, the existence of periodic wave solutions for functional differential equations was obtained by the use of an extension of coincidence degree theory (see [21], Theorem 3.1). We use the theorem belonging to [1] to obtain the existence of periodic wave solutions for Eq (1.1). To the best of our knowledge, there is no paper to use the theorem in [1] for studying the non-Newtonian filtration equations. 3, main results are obtained for the existence of periodic wave solutions to the non-Newtonian filtration equation (1.1).
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