Results 181 to 190 of about 2,044 (212)

Existence of global attractor of equations of Kirchhoff type

2015 11th International Conference on Natural Computation (ICNC), 2015
The paper focuses on existence of global attractors of equations of Kirchhoff type. Considering variational methods for appropriate equation space, and by integral inequality, Sobolev embedding theorem and equivalence theorem, this paper proves the existence of global attractors for the equation at the inner product space on the base of the global ...
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Remarks on an elliptic equation of Kirchhoff type

Nonlinear Analysis: Theory, Methods & Applications, 2005
Abstract We present a short survey on the nonlocal elliptic boundary value problem - M ∫ Ω | ∇ u | 2 d x Δ u = f ( x , u ) in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain of R N , M is a positive function, and f has subcritical growth.
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Critical Kirchhoff-type equation with singular potential

Topological Methods in Nonlinear Analysis, 2023
In this paper, we deal with the following Kirchhoff-type equation: \begin{equation*} -\bigg(1 +\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx\bigg) \Delta u +\frac{A}{|x|^{\alpha}}u =f(u),\quad x\in\mathbb{R}^{3}, \end{equation*} where $A> 0$ is a real parameter and $\alpha\in(0,1)\cup ({4}/{3},2)$.
Yu Su, Senli Liu
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Geometric optics for the Kirchhoff-type equations

Journal d'Analyse Mathématique, 2003
The author presents a method for finding small-amplitude, high-frequency wave solutions of Kirchhoff-type hyperbolic systems of nonlocal quasilinear partial differential equations. In this work, the author introduces his main result of the geometric optics on the asymptotic solutions of a first order symmetric strictly hyperbolic system by proving the ...
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Existence of Solution for a Singular Elliptic Equation of Kirchhoff Type

Mediterranean Journal of Mathematics, 2017
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Li, Qingwei, Gao, Wenjie, Han, Yuzhu
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Groundstates for Kirchhoff-Type Equations with Hartree-Type Nonlinearities

Results in Mathematics, 2019
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Li, Yan, Li, Xinfu, Ma, Shiwang
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A note about positive solutions for an equation of Kirchhoff type

Applied Mathematics and Computation, 2011
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André L. M. Martinez, Emerson V. Castelani, Jair da Silva, Wesley V. I. Shirabayashi   +3 more
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On a quasilinear Schrödinger–Kirchhoff-type equation with radial potentials

Nonlinear Analysis: Theory, Methods & Applications, 2013
The author investigates a quasilinear Schrödinger-Kirchhoff equation with radial potentials. The result is an application of the Mountain Pass Theorem and the symmetric Mountain Pass Theorem. The author shows existence of non trivial solutions of the problem \[ -\left(a+b\int_{R^N} |\nabla u|^p dx\right)^{p-1} \Delta_p u + V(|x|)|u|^{p-2}U =q(|x|)f(u) \
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Existence and multiplicity of solutions for Kirchhoff type equations

Nonlinear Analysis: Theory, Methods & Applications, 2011
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Sun, Ji-Jiang, Tang, Chun-Lei
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Quasilinear degenerate parabolic equations of Kirchhoff type

Mathematical Methods in the Applied Sciences, 1999
The main goal is to investigate the well-posedness of solutions of the abstract Kirchhoff equation \(u' + m(\| A^{1/2} u\|^2) A u =0\), \(u(0)=u_0\) in the Hilbert space \(H\). Here \(A:D(A)\subset H\to H\) is a selfadjoint nonnegative linear operator in \(H\).
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