The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method

2010 ◽  
Vol 73 (2) ◽  
pp. 440-449 ◽  
Author(s):  
Juntao Sun ◽  
Haibo Chen ◽  
Liu Yang
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Impulsive Differential Equation ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Two Parameters

The Neumann problem for the generalized Bagley-Torvik fractional differential equation

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Differential Equation ◽  
Neumann Problem ◽  
Fractional Differential Equation ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
The Neumann Problem

AbstractWe discuss the existence and multiplicity of solutions to the generalized Bagley-Torvik fractional differential equation

scholarly journals Weak Solutions for ap-Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Wei Dong
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Point Theory ◽  
Existence Of Weak Solutions

By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for ap-Laplacian impulsive differential equation with antiperiodic boundary conditions.

scholarly journals Weak Solutions for ap-Laplacian Impulsive Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wei Dong ◽  
Jiafa Xu ◽  
Xiaoyan Zhang
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Dirichlet Boundary ◽  
Point Theory ◽  
Existence Results ◽  
Dirichlet Boundary Conditions

By the virtue of variational method and critical point theory, we give some existence results of weak solutions for ap-Laplacian impulsive differential equation with Dirichlet boundary conditions.

scholarly journals Existence and multiplicity of solutions for anisotropic elliptic equation

2022 ◽  
Vol 40 ◽  
pp. 1-12
Author(s):  
El Amrouss Abdelrachid ◽  
Ali El Mahraoui
Keyword(s):  
Elliptic Equation ◽  
Variational Method ◽  
Nonlinear Problem ◽  
Multiplicity Of Solutions ◽  
Anisotropic Elliptic Equation ◽  
Existence And Multiplicity

In this article we study the nonlinear problem $$\left\{ \begin{array}{lr} -\sum_{i=1}^{N}\partial_{x_{i}}a_{i}(x,\partial_{x_{i}}u)+ b(x)~|u|^{P_{+}^{+}-2}u =\lambda f(x,u) \quad in \quad \Omega\\ u=0 \qquad on \qquad \partial\Omega \end{array} \right.$$ Using the variational method, under appropriate assumptions on $f$, we obtain a result on existence and multiplicity of solutions.

scholarly journals Existence of Solutions for a Robin Problem Involving thep(x)-Laplace Operator

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Mostafa Allaoui
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Laplace Operator ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Robin Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

In this article we study the nonlinear Robin boundary-value problem-Δp(x)u=f(x,u)  in  Ω,|∇u|px-2(∂u/∂ν)+β(x)up(x)-2u=0on∂Ω. Using the variational method, under appropriate assumptions onf, we obtain results on existence and multiplicity of solutions.

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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