Abstract
Motivated by the idea which has been introduced by Boulaaras and Guefaifia [S. Boulaaras and R. Guefaifia, Existence of positive weak solutions for a class of Kirchhoff elliptic systems with multiple parameters, Muth. Methods Appl. Sci. 41 (2018), no. 13, 5203-5210] and by Afrouzi and Shakeri [G. A. Afrouzi, S. Shakeri and N. T. Chung, Existence of positive solutions for variable exponent elliptic systems with multiple parameters, Afr. Mut. 26 (2015), no. 1-2, 159-168] combined with some properties of Kirchhoff-type operators, we prove the existence of positive solutions for a new class of nonlocal p(x)-Kirchhoff parabolic systems by using the sub- and super-solutions concept.