## 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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### References:

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