scholarly journals Existence of Multiple Solutions for a Quasilinear Biharmonic Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Wu Pan ◽  
Cheng-En Yu
Keyword(s):  
Critical Points ◽  
Multiple Solutions ◽  
Biharmonic Equation ◽  
Three Solutions

Using three critical points theorems, we prove the existence of at least three solutions for a quasilinear biharmonic equation.

Multiple solutions for a Dirichlet quasilinear system containing a parameter

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Shapour Heidarkhani ◽  
Johnny Henderson
Keyword(s):  
Differential Equations ◽  
Critical Points ◽  
Multiple Solutions ◽  
Second Order ◽  
Quasilinear System ◽  
Compact Interval ◽  
Three Solutions ◽  
Second Order Differential Equations

Abstract.In this paper, we apply two theorems from triple critical points theory to establish the existence of at least three solutions for the quasilinear second order differential equations on a compact interval

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.

Multiple solutions for Dirichlet impulsive equations

2014 ◽  
Vol 3 (S1) ◽  
pp. s89-s98 ◽  
Author(s):  
Massimiliano Ferrara ◽  
Shapour Heidarkhani ◽  
Pasquale F. Pizzimenti
Keyword(s):  
Banach Space ◽  
Boundary Conditions ◽  
Critical Points ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Reflexive Banach Space ◽  
Dirichlet Boundary Conditions ◽  
Nontrivial Solutions ◽  
Three Solutions ◽  
Impulsive Equations

AbstractIn this paper we are interested to ensure the existence of multiple nontrivial solutions for some classes of problems under Dirichlet boundary conditions with impulsive effects. More precisely, by using a suitable analytical setting, the existence of at least three solutions is proved exploiting a recent three-critical points result for smooth functionals defined in a reflexive Banach space. Our approach generalizes some well-known results in the classical framework.

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 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.

An existence result for multiple solutions to a Dirichlet problem

2017 ◽  
Vol 24 (1) ◽  
pp. 55-62
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi ◽  
John R. Graef
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Existence Result ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Three Solutions ◽  
Quasilinear Elliptic Problem ◽  
Critical Point Result ◽  
Quasilinear Elliptic

AbstractThe authors establish the existence of at least three solutions to a quasilinear elliptic problem subject to Dirichlet boundary conditions in a bounded domain in ${\mathbb{R}^{N}}$. A critical point result for differentiable functionals is used to prove the results.

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