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 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.

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.

scholarly journals Variational Approach for a Class of Two-point Fractional Boundary Value Systems

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 351-364
Author(s):  
Ghasem A. Afrouzi ◽  
Samad Mohseni Kolagar ◽  
Armin Hadjian ◽  
Jiafa Xu
Keyword(s):  
Critical Points ◽  
Variational Approach ◽  
Multiple Solutions ◽  
Existence Result ◽  
Boundary Value ◽  
Main Tool ◽  
Value Systems ◽  
Positive Parameter ◽  
Critical Set ◽  
Differentiable Functions

An existence result of multiple solutions for a class of two-point fractional boundary value equations depending upon a positive parameter is established. Our main tool is a three critical points theorem due to Bonanno and Marano [G. Bonanno and S.A. Marano,On the structure of the critical set of non-differentiable functions with a weakcompactness condition, Appl. Anal. 89 (2010), 1-10].

scholarly journals Multiplicity of solutions for perturbed nonlinear fractional p-Laplacian boundary value systems related with two control parameters

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2827-2848
Author(s):  
Jiabin Zuo ◽  
Rafik Guefaifia ◽  
Fares Kamache ◽  
Salah Boulaaras
Keyword(s):  
Variational Method ◽  
Critical Points ◽  
Weak Solutions ◽  
Boundary Value ◽  
Value Systems ◽  
Control Parameters ◽  
Differential Systems ◽  
Multiplicity Of Solutions ◽  
Three Critical Points Theorem ◽  
Perturbed Systems

This paper deals with the study of a class of perturbed nonlinear fractional p-Laplacian differential systems, where by using the variational method, two control parameters together with recent three critical points theorem by Bonanno and Candito for differentiable functionals for perturbed systems, the existence of three weak solutions has been proved.

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.

Variational approaches to systems of Sturm–Liouville boundary value problems

2020 ◽  
pp. 2150032
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Shahin Moradi
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Technical Approach ◽  
Three Solutions ◽  
Value System ◽  
Sturm Liouville ◽  
Variational Approaches

In this paper, we consider the existence of one solution and three solutions for the boundary value system with Sturm–Liouville boundary conditions [Formula: see text] for [Formula: see text]. Our technical approach is based on variational methods. In addition, examples are provided to illustrate our results.

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