scholarly journals Multiplicity of Solutions for Nonlocal Elliptic System of(p,q)-Kirchhoff Type

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Bitao Cheng ◽  
Xian Wu ◽  
Jun Liu
Keyword(s):  
Elliptic System ◽  
Critical Points ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Periodic Condition ◽  
Kirchhoff Type ◽  
Three Critical Points Theorem ◽  
Palais Smale Condition

This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type−[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω,−[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω,u=v=0, on∂Ω.Under bounded condition onMand some novel and periodic condition onF, some new results of the existence of two solutions and three solutions of the above mentioned nonlocal elliptic system are obtained by means of Bonanno's multiple critical points theorems without the Palais-Smale condition and Ricceri's three critical points theorem, respectively.

scholarly journals Multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations

2018 ◽  
Vol 5 (1) ◽  
pp. 76-88
Author(s):  
Stanislas Ouaro ◽  
Malick Zoungrana
Keyword(s):  
Critical Points ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Lipschitz Continuous ◽  
Three Critical Points Theorem ◽  
Existence And Multiplicity ◽  
Locally Lipschitz ◽  
Laplace Type ◽  
Locally Lipschitz Continuous

AbstractIn this article, we prove the existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations. We are interested in the existence of three solutions with the aid of linking arguments and using a three critical points theorem, for locally Lipschitz continuous fonctions.

scholarly journals Existence and multiplicity results for a Steklov problem involving (p(x), q(x))-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Belhadj Karim ◽  
A. Lakhdi ◽  
M. R. Sidi Ammi ◽  
A. Zerouali
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Laplacian Operator ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Steklov Problem ◽  
Three Critical Points Theorem ◽  
Existence And Multiplicity

Abstract In this work, we are concerned with a generalized Steklov problem with (p(x), q(x))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Qing-Mei Zhou ◽  
Ke-Qi Wang
Keyword(s):  
Eigenvalue Problem ◽  
Critical Points ◽  
Fractional Laplacian ◽  
Nonlinear Eigenvalue Problem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractIn this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in

scholarly journals On a class of non-local discrete boundary value problem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anass Ourraoui ◽  
Abdesslem Ayoujil
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Points ◽  
Boundary Value ◽  
Discrete Problem ◽  
Three Solutions ◽  
Content Type ◽  
Three Critical Points Theorem ◽  
Discrete Boundary Value Problem ◽  
Non Local

PurposeIn this article, the authors discuss the existence and multiplicity of solutions for an anisotropic discrete boundary value problem in T-dimensional Hilbert space. The approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.Design/methodology/approachThe approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.FindingsThe authors study the existence of results for a discrete problem, with two boundary conditions type. Accurately, the authors have proved the existence of at least three solutions.Originality/valueAn other feature is that problem is with non-local term, which makes some difficulties in the proof of our results.

Multiple solutions for elliptic resonant problems

2008 ◽  
Vol 138 (6) ◽  
pp. 1281-1289 ◽  
Author(s):  
Shibo Liu
Keyword(s):  
Critical Points ◽  
Multiple Solutions ◽  
Careful Analysis ◽  
Variational Functional ◽  
Three Critical Points Theorem ◽  
Semilinear Elliptic ◽  
Palais Smale Condition

Two non-trivial solutions for semilinear elliptic resonant problems are obtained via the Lyapunov—Schmidt reduction and the three-critical-points theorem. The difficulty that the variational functional does not satisfy the Palais—Smale condition is overcome by taking advantage of the reduction and a careful analysis of the reduced functional.

scholarly journals Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional -Laplacian Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Shapour Heidarkhani
Keyword(s):  
Critical Points ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Value Systems ◽  
Laplacian Operator ◽  
Three Solutions ◽  
Value System ◽  
One Dimensional ◽  
Multipoint Boundary ◽  
Three Critical Points Theorem

Employing a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system in , , for , is established.

scholarly journals A non-smooth three critical points theorem for general hemivariational inequality on bounded domains

2017 ◽  
Vol 35 (3) ◽  
pp. 95-110
Author(s):  
Fariba Fattahi
Keyword(s):  
Boundary Condition ◽  
Critical Points ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Hemivariational Inequality ◽  
Bounded Domains ◽  
Three Solutions ◽  
Three Critical Points Theorem

In this paper we are concerned with the study of a hemivariationalinequality with nonhomogeneous Neumann boundary condition. Weestablish the existence of at least three solutions of the problem by usingthe nonsmooth three critical points theorem and the principle of symmetriccriticality for Motreanu-Panagiotopoulos type functionals.

Three solutions for a nonlocal fractional p-Kirchhoff type elliptic system

2019 ◽  
pp. 1-18 ◽  
Author(s):  
Elhoussine Azroul ◽  
Abdelmoujib Benkirane ◽  
Athmane Boumazourh ◽  
Mohammed Srati
Keyword(s):  
Elliptic System ◽  
Three Solutions ◽  
Kirchhoff Type

scholarly journals MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATION VIA VARIATIONAL METHODS

2010 ◽  
Vol 82 (3) ◽  
pp. 446-458 ◽  
Author(s):  
JUNTAO SUN ◽  
HAIBO CHEN ◽  
TIEJUN ZHOU
Keyword(s):  
Differential Equation ◽  
Variational Methods ◽  
Fourth Order ◽  
Critical Points ◽  
Impulsive Differential Equation ◽  
Classical Solutions ◽  
Multiplicity Of Solutions ◽  
Three Critical Points Theorem ◽  
New Criteria

AbstractIn this paper, we deal with the multiplicity of solutions for a fourth-order impulsive differential equation with a parameter. Using variational methods and a ‘three critical points’ theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. An example is also given in order to illustrate the main results.

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