A parabolic problem of Kirchhoff type with gradient term and nonlinear boundary condition

Eugenio Cabanillas Lapa

Abstract


The object of this work is to study the existence of weak solutions for (p1(x), p2(x))-Laplacian parabolic Kirchhoff equation. We apply degree theory to operators of the type T + S + C, where T is maximal monotone, S is bounded pseudomonotone, and C is compact with D(T) ⊆ D(C) and satisfies a sublinearity condition, to get our result within the context of Sobolev spaces with variable exponents.

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DOI: https://doi.org/10.52846/ami.v52i2.2025