scholarly journals Existence results for a sublinear second order Dirichlet boundary value problem on the half-line

2020 ◽  
Vol 40 (5) ◽  
pp. 537-548
Author(s):  
Dahmane Bouafia ◽  
Toufik Moussaoui
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Half Line ◽  
Dirichlet Boundary Value Problem ◽  
Nontrivial Solutions

In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland's variational principle and critical point theory.

scholarly journals Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Jigen Peng
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Of Solution ◽  
Dirichlet Boundary Value Problem ◽  
Condensing Mapping

The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

scholarly journals Existence theory for single and multiple solutions to semipositone discrete Dirichlet boundary value problems with singular dependent nonlinearities

2003 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Daqing Jiang ◽  
Lili Zhang ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Existence Theory ◽  
Dirichlet Boundary Value Problem

In this paper we establish the existence of single and multiple solutions to the semipositone discrete Dirichlet boundary value problem {Δ2y(i−1)+μf(i,y(i))=0,            i∈{1,2,…,T}y(0)=y(T+1)=0, where μ>0 is a constant and our nonlinear term f(i,u) may be singular at u=0.

scholarly journals Some Existence Results of Positive Solutions forφ-Laplacian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xianghui Xu ◽  
Yong-Hoon Lee
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Dirichlet Boundary Value Problem ◽  
Singular Weight ◽  
Existence Of Positive Solutions

We study the existence of positive solutions for the homogeneous Dirichlet boundary value problem ofφ-Laplacian systems with a singular weight which may not be inL1.

scholarly journals Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shaohong Wang ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Strong Maximum Principle ◽  
Dirichlet Boundary Value Problem ◽  
Partial Difference Equation ◽  
Three Solutions ◽  
Partial Difference

AbstractBy employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give precise estimates of the parameter to guarantee that the considered problem possesses at least three solutions. Furthermore, based on a strong maximum principle, we show that two of the obtained solutions are positive under some suitable assumptions of the nonlinearity.

scholarly journals Weak Solutions for a Second Order Dirichlet Boundary Value Problem on Time Scale

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wandong Lou
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Existence Theorems ◽  
Boundary Value ◽  
Degree Theory ◽  
Point Theory ◽  
Second Order ◽  
Dirichlet Boundary Value Problem

We adopt the Leray-Schauder degree theory and critical point theory to consider a second order Dirichlet boundary value problem on time scales and obtain some existence theorems of weak solutions for the previous problem.

scholarly journals Infinitely Many Solutions for Discrete Boundary Value Problems with the p , q -Laplacian Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhuomin Zhang ◽  
Zhan Zhou
Keyword(s):  
Maximum Principle ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Theory ◽  
Strong Maximum Principle ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Multiplicity

In this paper, we consider the existence and multiplicity of solutions for a discrete Dirichlet boundary value problem involving the p , q -Laplacian. By using the critical point theory, we obtain the existence of infinitely many solutions under some suitable assumptions on the nonlinear term. Also, by our strong maximum principle, we can obtain the existence of infinitely many positive solutions.

scholarly journals Nontrivial Solutions for a Boundary Value Problem of nth-Order Impulsive Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jiafa Xu ◽  
Zhongli Wei
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Impulsive Differential Equation ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Degree Theory ◽  
Impulsive Effects ◽  
Nontrivial Solutions

We study the existence of nontrivial solutions for nth-order boundary value problem with impulsive effects. We utilize Leray-Schauder degree theory to establish our main results. Furthermore, our nonlinear term f is allowed to grow superlinearly and sublinearly.

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