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We consider the global solvability to the Cauchy problem of Kirchhoff equation with generalized classes of Manfrins class. Manfrins class is a subclass of Sobolev space, but we shall extend this class as a subclass of the ultradifferentiable class, and we succeed to prove the global solvability of Kirchhoff equation with large data in wider classes from the previous works.
This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior
We study the non-existence, existence and multiplicity of positive solutions to the following nonlinear Kirchhoff equation:% begin{equation*} left{ begin{array}{l} -Mleft( int_{mathbb{R}^{3}}leftvert abla urightvert ^{2}dxright) Delta u+mu Vleft( xr
The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. T
For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly,
This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space $gamma^s_{eta,L^2}$. Furthermore, similar results are obtained for the initial-boundary value problems in bounded domains and in exterior domains with compact boundary.