scholarly journals ON AN ELLIPTIC SYSTEM OF P(X)-KIRCHHOFF-TYPE UNDER NEUMANN BOUNDARY CONDITION

2012 ◽  
Vol 17 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Zehra Yucedag ◽  
Mustafa Avci ◽  
Rabil Mashiyev
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Principle ◽  
Variational Method ◽  
Elliptic System ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Kirchhoff Type ◽  
Direct Variational Method

In the present paper, by using the direct variational method and the Ekeland variational principle, we study the existence of solutions for an elliptic system of p(x)-Kirchhoff-type under Neumann boundary condition and show the existence of a weak solution.

scholarly journals A Class of Variable-Order Fractional p · -Kirchhoff-Type Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Yong Wu ◽  
Zhenhua Qiao ◽  
Mohamed Karim Hamdani ◽  
Bingyu Kou ◽  
Libo Yang
Keyword(s):  
Weak Solution ◽  
Variational Principle ◽  
Variational Method ◽  
Elliptic System ◽  
Type Systems ◽  
Ekeland Variational Principle ◽  
Variable Order ◽  
Variable Exponents ◽  
Kirchhoff Type ◽  
Direct Variational Method

This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional p x -operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak solution. This is our first attempt to study this kind of system, in the case of variable-order fractional variable exponents. Our main theorem extends in several directions previous results.

Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moloud Makvand Chaharlang ◽  
Abdolrahman Razani
Keyword(s):  
Boundary Condition ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Neumann Boundary Condition ◽  
Mountain Pass Theorem ◽  
Minimum Principle ◽  
Neumann Boundary ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

AbstractIn this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces.

scholarly journals Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problems

2014 ◽  
Vol 33 (2) ◽  
pp. 203-217 ◽  
Author(s):  
El Miloud Hssini ◽  
Mohammed Massar ◽  
Najib Tsouli
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Technical Approach ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problems

This paper is concerned with the existence and multiplicity of solutions for a class of $p(x)$-Kirchhoff type equations with Neumann boundary condition. Our technical approach is based on variational methods.

Existence of a solution for a nonlocal elliptic system of (p(x),q(x))-Kirchhoff type

2018 ◽  
Vol 9 (3) ◽  
pp. 221-233
Author(s):  
Ali Taghavi ◽  
Horieh Ghorbani
Keyword(s):  
Weak Solution ◽  
Variational Principle ◽  
Variational Methods ◽  
Elliptic System ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Continuous Functions ◽  
Ekeland's Variational Principle ◽  
Existence Of A Solution ◽  
Kirchhoff Type

Abstract In this paper, we consider the system \left\{\begin{aligned} &\displaystyle{-}M_{1}\bigg{(}\int_{\Omega}\frac{\lvert% \nabla u\rvert^{p(x)}+\lvert u\rvert^{p(x)}}{p(x)}\,dx\biggr{)}(\Delta_{p(x)}u% -\lvert u\rvert^{p(x)-2}u)=\lambda a(x)\lvert u\rvert^{r_{1}(x)-2}u-\mu b(x)% \lvert u\rvert^{\alpha(x)-2}u&&\displaystyle\text{in }\Omega,\\ &\displaystyle{-}M_{2}\bigg{(}\int_{\Omega}\frac{\lvert\nabla v\rvert^{q(x)}+% \lvert v\rvert^{q(x)}}{q(x)}\,dx\biggr{)}(\Delta_{q(x)}v-\lvert v\rvert^{q(x)-% 2}v)=\lambda c(x)\lvert v\rvert^{r_{2}(x)-2}v-\mu d(x)\lvert v\rvert^{\beta(x)% -2}v&&\displaystyle\text{in }\Omega,\\ &\displaystyle u=v=0&&\displaystyle\text{on }\partial\Omega,\end{aligned}\right. where Ω is a bounded domain in {\mathbb{R}^{N}} ( {N\geq 2} ) with a smooth boundary {\partial\Omega} , {M_{1}(t),M_{2}(t)} are continuous functions and {\lambda,\mu>0} . We prove that for any {\mu>0} there exists {\lambda_{*}} sufficiently small such that for any {\lambda\in(0,\lambda_{*})} the above system has a nontrivial weak solution. The proof relies on some variational arguments based on Ekeland’s variational principle, and some adequate variational methods.

scholarly journals Existence of solutions for an elliptic p(x)-Kirchhoff-type systems in unbounded domain

2018 ◽  
Vol 36 (3) ◽  
pp. 193-205 ◽  
Author(s):  
Abdelamlek Brahim ◽  
Ali Djellit ◽  
Saadia Tas
Keyword(s):  
Variational Method ◽  
Elliptic System ◽  
Unbounded Domain ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Main Tool ◽  
Type Systems ◽  
Mountain Pass ◽  
Nonlocal Term ◽  
Kirchhoff Type

In this paper we study of the existence of solutions for a class of elliptic system with nonlocal term in R^{N}. The main tool used is the variational method, more precisely, the Mountain Pass Theorem.

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