scholarly journals Multiple Solutions for Elliptic px,qx-Kirchhoff-Type Potential Systems in Unbounded Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Nabil Chems Eddine ◽  
Abderrahmane El Hachimi
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Unbounded Domains ◽  
Critical Point Theorem ◽  
Kirchhoff Type ◽  
Double Eigenvalue ◽  
Potential System ◽  
Type Potential

In this paper, we establish the existence of at least three weak solutions for a parametric double eigenvalue quasi-linear elliptic px,qx-Kirchhoff-type potential system. Our approach is based on a variational method, and a three critical point theorem is obtained by Bonano and Marano.

scholarly journals Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations onRN

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yu Duan ◽  
Chun-Lei Tang
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Multiple Solutions ◽  
Asymptotically Linear ◽  
Kirchhoff Type ◽  
Multiplicity Of Positive Solutions

The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameterλonRNis proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity andλ>0is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of three positive solutions.

Multiplicity results for elliptic Kirchhoff-type problems

2017 ◽  
Vol 6 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Sami Baraket ◽  
Giovanni Molica Bisci
Keyword(s):  
Weak Solutions ◽  
Multiple Solutions ◽  
Fractional Operators ◽  
Type Problem ◽  
Small Perturbations ◽  
Multiplicity Results ◽  
Nonlinear Part ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Kirchhoff Type Problems

AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.

scholarly journals Existence of Multiple Solutions for Second-Order Problem with Stieltjes Integral Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Qing-Qing Hu ◽  
Baoqiang Yan
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Multiple Solutions ◽  
Order Equation ◽  
Second Order ◽  
Integral Boundary Condition ◽  
Stieltjes Integral ◽  
Order Problem ◽  
Integral Boundary ◽  
Critical Point Theorem

In this paper, we consider the existence of multiple solutions for second-order equation with Stieltjes integral boundary condition using the three-critical-point theorem and variational method. Firstly, a novel space is established and proved to be Hilbert one. Secondly, based on the above work, we obtain the existence of multiple solutions for our problem. Finally, in order to illustrate the effectiveness of our problem better, the example is listed.

scholarly journals EXISTENCE OF 3-WEAK SOLUTIONS FOR A NEW CLASS OF AN OVERDETERMINED SYSTEM OF FRACTIONAL PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040036 ◽  
Author(s):  
SALAH BOULAARAS ◽  
RAFIK GUEFAIFIA ◽  
ASMA ALHARBI ◽  
BAHRI CHERIF
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Differential System ◽  
Point Theorem ◽  
Weak Solutions ◽  
Overdetermined System ◽  
Critical Point Theorem ◽  
New Class

The paper deals with the existence of three different weak solutions of [Formula: see text] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

scholarly journals Weak Solutions for ap-Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Wei Dong
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Point Theory ◽  
Existence Of Weak Solutions

By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for ap-Laplacian impulsive differential equation with antiperiodic boundary conditions.

scholarly journals Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Armin Hadjian ◽  
Saleh Shakeri
Keyword(s):  
Multiple Solutions ◽  
Main Tool ◽  
Elliptic Systems ◽  
Existence Results ◽  
Laplacian Operator ◽  
Quasilinear Elliptic System ◽  
Critical Point Theorem ◽  
Quasilinear Elliptic Systems ◽  
Double Eigenvalue ◽  
Quasilinear Elliptic

Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.

scholarly journals A Class of Critical Magnetic Fractional Kirchhoff Problems

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 76 ◽  
Author(s):  
Jiabin Zuo ◽  
Tianqing An ◽  
Guoju Ye
Keyword(s):  
Asymptotic Behavior ◽  
Critical Point ◽  
Electromagnetic Fields ◽  
Point Theorem ◽  
Asymptotic Behavior Of Solutions ◽  
Critical Nonlinearity ◽  
Type Problem ◽  
Critical Point Theorem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

In this paper, we deal with the existence and asymptotic behavior of solutions for a fractional Kirchhoff type problem involving the electromagnetic fields and critical nonlinearity by using the classical critical point theorem. Meanwhile, an example is given to illustrate the application of the main result.

scholarly journals Infinitely many weak solutions for some elliptic problems in RN

2016 ◽  
Vol 100 (114) ◽  
pp. 271-278
Author(s):  
Mehdi Khodabakhshi ◽  
Abdolmohammad Aminpour ◽  
Mohamad Tavani
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Elliptic Problems ◽  
Point Theory

We investigate the existence of infinitely many weak solutions to some elliptic problems involving the p-Laplacian in RN by using variational method and critical point theory.

scholarly journals Twoweak solutions for a singular (p,q)-Laplacian problem

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3399-3407 ◽  
Author(s):  
F. Behboudi ◽  
A. Razani
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Laplacian Operator ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Smooth Bounded Domain

Here, a singular boundary value problem involving the (p,q)-Laplacian operator in a smooth bounded domain in RN is considered. Using the variational method and critical point theory, the existence of two weak solutions is proved.

The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach

2019 ◽  
Vol 20 (3-4) ◽  
pp. 361-371
Author(s):  
Dongping Li ◽  
Fangqi Chen ◽  
Yukun An
Keyword(s):  
Variational Methods ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Point Theorem ◽  
Weak Solutions ◽  
Variational Approach ◽  
Dirichlet Boundary ◽  
Coupled Systems ◽  
Critical Point Theorem ◽  
Two Parameters

AbstractIn this paper, by using variational methods and a critical point theorem due to Bonanno and Marano, the existence of at least three weak solutions is obtained for a class of p-Laplacian type nonlinear fractional coupled systems depending on two parameters. Two examples are given to illustrate the applications of our main results.

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