Results 11 to 20 of about 3,079 (223)
On a Kirchhoff Equation in Bounded Domains
Advanced Nonlinear Studies, 2018 In this paper, we consider the following Kirchhoff equation:
Huang Yisheng, Wu Yuanze
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On isolated singularities of Kirchhoff equations [PDF]
Advances in Nonlinear Analysis, 2020 In this note, we study isolated singular positive solutions of Kirchhoff ...
Chen Huyuan +2 more
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On the Normal Form of the Kirchhoff Equation [PDF]
Journal of Dynamics and Differential Equations, 2020 AbstractConsider the Kirchhoff equation $$\begin{aligned} \partial _{tt} u - \Delta u \Big ( 1 + \int _{\mathbb {T}^d} |\nabla u|^2 \Big ) = 0 \end{aligned}$$ ∂
BALDI, Pietro, HAUS, Emanuele
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Optimal Control of the Kirchhoff Equation
CoRR, 2021 We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-order ...
Masoumeh Hashemi +2 more
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On the critical $p$-Kirchhoff equation
Topological Methods in Nonlinear Analysis, 2023 We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for the $(\text{PS})$ condition to hold. Then we prove some existence and multiplicity results using tools from Morse theory, in particular, the notion of a cohomological local splitting and eigenvalues based on the
Erisa Hasani, Kanishka Perera
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On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations [PDF]
Regular and Chaotic Dynamics, 2012 It is proven that the general Kirchhoff case of the Kirchhoff equations for $B\ne 0$ is not algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on $e(4)$ with the standard Lie-Poisson bracket.
Dragović, Vladimir, Gajić, Borislav
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Nonlinear perturbations of the Kirchhoff equation
Electronic Journal of Differential Equations, 2017 In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation $$\displaylines{ u'' - M(t,\|u(t)\|^{2})\Delta u + |u|^{\rho} =f \quad\text{in } \Omega \times (0, T_0), \cr u=
Manuel Milla Miranda +2 more
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Optimal control of the stationary Kirchhoff equation
Computational Optimization and Applications, 2023 AbstractWe consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-
Masoumeh Hashemi +2 more
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Multiplicity of Solutions for an Elliptic Kirchhoff Equation
Milan Journal of Mathematics, 2022 AbstractIn this paper we study the existence of positive solution to the Kirchhoff elliptic problem $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\left( 1+\gamma G'\left( \Vert \nabla u\Vert ^2_{L^2(\Omega )}\right) \right) \Delta u = \lambda f(u) &{} \text{ in } \; \Omega ,\\ u = 0 &{} \text{ on } \; \partial \Omega ,\\ \end ...
Arcoya, David +2 more
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Global Well-Posedness of the Kirchhoff Equation and Kirchhoff Systems [PDF]
, 2014 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 domains with compact boundary.
Matsuyama, T, Ruzhansky, M
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