Results 11 to 20 of about 2,044 (212)

Global solutions for a nonlinear Kirchhoff type equation with viscosity [PDF]

Opuscula Mathematica, 2023
In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem \[u_{tt}- M\left(\,\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u - \delta\triangle u_{t}= \mu|u|^{\rho-2}u ...
Eugenio Cabanillas Lapa
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Existence, multiplicity and nonexistence results for Kirchhoff type equations

Advances in Nonlinear Analysis, 2020
In this paper, we study following Kirchhoff type equation:
He Wei, Qin Dongdong, Wu Qingfang
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Global bifurcation and nodal solutions for homogeneous Kirchhoff type equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper, we shall study unilateral global bifurcation phenomenon for the following homogeneous Kirchhoff type problem \begin{equation*} \begin{cases} -\left(\int_0^1 \left\vert u'\right\vert^2\,dx\right)u''=\lambda u^3+h(x,u,\lambda)&\text{in}\,\, (
Fang Liu, Hua Luo, Guowei Dai
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Stability of Solutions for a Krichhoff-Type Plate Equation with Degenerate Damping

Communications in Advanced Mathematical Sciences, 2022
We investigate a Kirchhoff type plate equation with degenerate damping term. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping.
Fatma Ekinci, Erhan Pişkin
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An Existence Result for Fractional Kirchhoff-Type Equations

Zeitschrift für Analysis und ihre Anwendungen, 2016
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
Bisci, G., TULONE, Francesco
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Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems

International Journal of Differential Equations, 2019
We consider a damped Kirchhoff-type equation with Dirichlet boundary conditions. The objective is to show the Fréchet differentiability of a nonlinear solution map from a bilinear control input to the solution of a Kirchhoff-type equation.
Jin-soo Hwang
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Multiple Sign-Changing Solutions for Kirchhoff-Type Equations [PDF]

Discrete Dynamics in Nature and Society, 2015
We study the following Kirchhoff-type equations-a+b∫Ω∇u2dxΔu+Vxu=fx,u, inΩ,u=0, in∂Ω, whereΩis a bounded smooth domain ofRN  (N=1,2,3),a>0,b≥0,f∈C(Ω¯×R,R), andV∈C(Ω¯,R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing.
Xingping Li, Xiumei He
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Existence of nontrivial solutions for p-Kirchhoff type equations [PDF]

Boundary Value Problems, 2013
The authors make use of the linking theorem and the mountain pass theorem to show the existence of nontrivial solutions for the nonlocal elliptic \(p\)-Kirchhoff equations without assuming Ambrosetti-Rabinowitz type growth conditions. At least one nontrivial weak solution, in the space \(W_0^{1,p}(\Omega),\) is obtained. The weak solutions of the above
Liu, Chunhan, Wang, Jianguo, Gao, Qingling   +2 more
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Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents

Journal of Mathematical Sciences and Modelling, 2023
This paper deals with a parabolic-type Kirchhoff equation with variable exponents. Firstly, we obtain the global existence of solutions by Faedo-Galerkin method. Later, we prove the decay of solutions by Komornik's inequality.
Gülistan Butakın, Erhan Pişkin
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Blow up results for a viscoelastic Kirchhoff-type equation with logarithmic nonlinearity and strong damping [PDF]

Mathematica Moravica, 2021
A Kirchhoff equation type with memory term competing with a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for the initial data in a stability set created from Nehari Manifold and prove blow
Ferreira Jorge, Pışk˙ın Erhan, Irkıl Nazlı, Raposo Carlos A.   +3 more
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