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Existence of solutions for \(p\)-Laplacian parabolic Kirchhoff equation. (English) Zbl 1476.35129

Summary: In this paper, by the Leray-Schauder principle, we study the existence of solutions for the following \(p\)-Laplacian Kirchhoff equation \[ u_t - ( 1 + \| \nabla u \|_{L^p ( \Omega )}^p ) \Delta_p u + g ( u ) = 0 \] on a bounded domain \(\Omega \subset \mathbb{R}^N\) with initial-boundary conditions.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35K20 Initial-boundary value problems for second-order parabolic equations
35R09 Integro-partial differential equations
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