scholarly journals On the compactness threshold in the critical Kirchhoff equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Erisa Hasani ◽  
Kanishka Perera
Keyword(s):  
Closed Form ◽  
Threshold Level ◽  
Kirchhoff Equation ◽  
Nonlocal Term ◽  
Main Difficulty ◽  
Variational Characterization ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Closed Form Formula

<p style='text-indent:20px;'>We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.</p>

A closed-form formula characterization of the Epps effect

2019 ◽  
Vol 20 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Giuseppe Buccheri ◽  
Giulia Livieri ◽  
Davide Pirino ◽  
Alessandro Pollastri
Keyword(s):  
Closed Form ◽  
Closed Form Formula

scholarly journals Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Pawan K. Mishra ◽  
Konijeti Sreenadh
Keyword(s):  
Kirchhoff Equation ◽  
Multiplicity Results ◽  
Existence And Multiplicity

AbstractIn this paper, we show the existence and multiplicity of nontrivial non-negative solutions of the fractional

On a Kirchhoff Equation in Bounded Domains

2018 ◽  
Vol 18 (3) ◽  
pp. 613-648
Author(s):  
Yisheng Huang ◽  
Yuanze Wu
Keyword(s):  
Variational Method ◽  
Smooth Boundary ◽  
Uniqueness Result ◽  
Kirchhoff Equation ◽  
Bounded Domains ◽  
Multiplicity Results ◽  
Nodal Domains ◽  
Existence And Multiplicity ◽  
Sobolev Exponent ◽  
Sign Changing Solutions

AbstractIn this paper, we consider the following Kirchhoff equation:\left\{\begin{aligned} &\displaystyle{-}\bigg{(}a+b\int_{\Omega}\lvert\nabla u% |^{2}\,dx\bigg{)}\Delta u=\lambda u+|u|^{p-2}u&&\displaystyle\text{in }\Omega,% \\ &\displaystyle u=0&&\displaystyle\text{on }\partial\Omega,\end{aligned}\right.where{\Omega\subset\mathbb{R}^{N}}({N\geq 3}) is a bounded domain with smooth boundary{\partial\Omega},{2<p<2^{*}=\frac{2N}{N-2}}is the Sobolev exponent anda,b, λ are positive parameters. By the variational method, we obtain some existence and multiplicity results of the sign-changing solutions (including the radial sign-changing solution in the case of{\Omega=\mathbb{B}_{R}}) for this problem. Some further properties of these sign-changing solutions, such as the numbers of the nodal domains, the concentration behaviors as{b\to 0^{+}}, the estimates of the energy values and so on, are also obtained. Our results generalize and improve some known results in the literature. Moreover, we also obtain a uniqueness result of the radial positive solution.

scholarly journals ON THE REPRESENTATION OF THE NESTED LOGIT MODEL

2021 ◽  
pp. 1-11
Author(s):  
Alfred Galichon
Keyword(s):  
Closed Form ◽  
Logit Model ◽  
Random Variables ◽  
Nested Logit ◽  
Random Utility ◽  
Nested Logit Model ◽  
Utility Representation ◽  
Phd Thesis ◽  
Closed Form Formula

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

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