scholarly journals Multiplicity of solutions for the discrete boundary value problem involving the p-Laplacian

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Design Methodology ◽  
Boundary Value ◽  
Point Theory ◽  
Content Type ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

PurposeThe purpose of this paper is the study of existence and multiplicity of solutions for a nonlinear discrete boundary value problems involving the p-laplacian.Design/methodology/approachThe approach is based on variational methods and critical point theory.FindingsTheorem 1.1. Theorem 1.2. Theorem 1.3. Theorem 1.4.Originality/valueThe paper is original and the authors think the results are new.

scholarly journals Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chunyan He ◽  
Yongzhi Liao ◽  
Yongkun Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We investigate the existence and multiplicity of solutions to a boundary value problem for impulsive differential equations. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, at least two solutions, and infinitely many solutions. Some examples are given to illustrate the effectiveness of our results.

scholarly journals A Variational Approach to Perturbed Discrete Anisotropic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Amjad Salari ◽  
Giuseppe Caristi ◽  
David Barilla ◽  
Alfio Puglisi
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Results ◽  
Anisotropic Equation

We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

scholarly journals Some remarks on nonlinear discrete boundary value problems

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Marek Galewski ◽  
Joanna Smejda
Keyword(s):  
Nonlinear System ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Monotonicity Results

AbstractUsing critical point theory and some monotonicity results we consider the existence and multiplicity of solutions to nonlinear discrete boundary value problems represented as a nonlinear system

scholarly journals Existence and Multiplicity of Solutions for a Biharmonic Equation with p(x)-Kirchhoff Type

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Sobolev Space ◽  
Critical Point ◽  
Critical Point Theory ◽  
Elliptic Equations ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity

Based on the basic theory and critical point theory of variable exponential Lebesgue Sobolev space, this paper investigates the existence and multiplicity of solutions for a class of nonlocal elliptic equations with Navier boundary value conditions when (AR) condition does not hold and improves or generalizes the original conclusions.

scholarly journals Multiple positive solutions for periodic boundary value problem via variational methods

2008 ◽  
Vol 39 (2) ◽  
pp. 111-120 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Periodic Boundary Value Problem ◽  
Multiple Positive Solutions

In this paper, we investigate the positive solutions of periodic boundary value problem. By using critical point theory the existence of multiple positive solutions is obtained.

scholarly journals Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 475 ◽  
Author(s):  
Fares Kamache ◽  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Asma Alharbi
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Existence Of Weak Solutions ◽  
New Class ◽  
Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

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