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 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.

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 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.

Sign in / Sign up

Export Citation Format

Share Document