scholarly journals Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory

2011 ◽  
Vol 53 (9-10) ◽  
pp. 1844-1855 ◽  
Author(s):  
Liang Bai ◽  
Binxiang Dai
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Impulsive Boundary Value Problem

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 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 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.

EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY

2012 ◽  
Vol 22 (04) ◽  
pp. 1250086 ◽  
Author(s):  
FENG JIAO ◽  
YONG ZHOU
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Fractional Boundary Value Problem ◽  
Fractional Differential ◽  
Left And Right ◽  
First Time

In this paper, by the critical point theory, the boundary value problem is discussed for a fractional differential equation containing the left and right fractional derivative operators, and various criteria on the existence of solutions are obtained. To the authors' knowledge, this is the first time, the existence of solutions to the fractional boundary value problem is dealt with by using critical point theory.

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