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Existence of positive solutions for a new class of Kirchhoff parabolic systems. (English) Zbl 1443.35075
Summary: We study the existence of weak positive solutions for a new class of Kirchhoff parabolic systems in bounded domains with multiple parameters taking into account the symmetry conditions and the right-hand side defined as a multiplication of two separate functions. Our results are natural extensions of previous results in the field, which used the same method for some classical elliptic equations.

MSC:
35K57 Reaction-diffusion equations
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
35D30 Weak solutions to PDEs
35J62 Quasilinear elliptic equations
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