scholarly journals Existence and multiplicity of solutions to the Navier boundary value problem for a class of (p(x),q(x))-biharmonic systems

2020 ◽  
Vol 65 (2) ◽  
pp. 229-241
Author(s):  
Belaouidel Hassan ◽  
◽  
Anass Ourraoui ◽  
Najib Tsouli ◽  
◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity of Solutions for a Periodic Hill's Equation with Parametric Dependence and Singularities

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Alberto Cabada ◽  
José Ángel Cid
Keyword(s):  
Boundary Value Problem ◽  
Green's Function ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Positive Parameter ◽  
Hill’S Equation ◽  
Parametric Dependence ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We deal with the existence and multiplicity of solutions for the periodic boundary value problemx″(t)+a(t)x(t)=λg(t)f(x)+c(t), x(0)=x(T), x′(0)=x′(T), whereλis a positive parameter. The functionf:(0,∞)→(0,∞)is allowed to be singular, and the related Green's function is nonnegative and can vanish at some points.

On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Diego Averna ◽  
Stepan Tersian ◽  
Elisabetta Tornatore
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Nonnegative Solutions ◽  
Fractional Differential ◽  
Dirichlet’S Problem

AbstractIn this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

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 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 Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

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