Existence of positive solutions of a new class of nonlocal \(p(x)\)-Kirchhoff parabolic systems via sub-super-solutions concept. (English) Zbl 1448.35294
Summary: Motivated by the idea which has been introduced by the second and the third author [Math. Methods Appl. Sci. 41, No. 13, 5203–5210 (2018; Zbl 1397.35096)]
and by G. A. Afrouzi et al. [Afr. Mat. 26, No. 1–2, 159–168 (2015; Zbl 1311.35104)] 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.
MSC:
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K59 | Quasilinear parabolic equations |
| 35K55 | Nonlinear parabolic equations |
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