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 On singularly weighted generalized Laplacian systems and their applications

2018 ◽  
Vol 7 (2) ◽  
pp. 149-165 ◽  
Author(s):  
Xianghui Xu ◽  
Yong-Hoon Lee
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Asymptotic Behaviors ◽  
Singular Weight ◽  
Existence And Nonexistence ◽  
Generalized Laplacian

AbstractWe study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be integrable. Some explicit intervals which correspond to the existence and nonexistence of positive solutions for the system with the finite asymptotic behaviors of the nonlinearities at 0 and {\infty} are obtained.

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 Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min Zhao ◽  
Yongping Sun
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Monotone Iterative Method ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problem

We study the existence of positive solutions for a nonlinear higher-order multipoint boundary value problem. By applying a monotone iterative method, some existence results of positive solutions are obtained. The main result is illustrated with an example.

Existence and Multiplicity of Positive Solutions for a Dirichlet Boundary Value Problem in ℝ2

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
V. Barutello ◽  
A. Capietto ◽  
P. Habets
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Parameter Dependent ◽  
Vector Differential Equation

AbstractWe deal with the Dirichlet boundary value problem associated to a parameter-dependent second order vector differential equation. Using the method of lower and upper solutions together with degree theory, we provide existence and multiplicity of positive solutions.

scholarly journals On the existence of multiple solutions for a partial discrete Dirichlet boundary value problem with mean curvature operator

2021 ◽  
Vol 11 (1) ◽  
pp. 198-211
Author(s):  
Sijia Du ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Mean Curvature ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Curvature Operator ◽  
Dirichlet Boundary Value Problem ◽  
The Maximum Principle ◽  
Mean Curvature Operator

Abstract Apartial discrete Dirichlet boundary value problem involving mean curvature operator is concerned in this paper. Under proper assumptions on the nonlinear term, we obtain some feasible conditions on the existence of multiple solutions by the method of critical point theory. We further separately determine open intervals of the parameter to attain at least two positive solutions and an unbounded sequence of positive solutions with the help of the maximum principle.

scholarly journals Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Functional Differential

We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained.

scholarly journals Positive Solutions of a General Discrete Dirichlet Boundary Value Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xinfu Li ◽  
Guang Zhang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Finite Lattice ◽  
State Equation ◽  
Heat Diffusion ◽  
Dirichlet Boundary Value Problem ◽  
Monotone Method ◽  
The Maximum Principle

A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on anyn-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

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