scholarly journals Positive solutions for some discrete semipositone problems via bifurcation theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Man Xu ◽  
Ruyun Ma
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

scholarly journals Bifurcation for some quasilinear operators

2001 ◽  
Vol 131 (4) ◽  
pp. 733-765 ◽  
Author(s):  
David Arcoya ◽  
José Carmona ◽  
Benedetta Pellacci
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Smooth Boundary ◽  
Elliptic Boundary ◽  
Complete Analysis ◽  
Multiplicity Results ◽  
Elliptic Boundary Value ◽  
The Matrix ◽  
Image Position ◽  
Quasilinear Elliptic

This paper deals with existence, uniqueness and multiplicity results of positive solutions for the quasilinear elliptic boundary-value problem , where Ω is a bounded open domain in RN with smooth boundary. Under suitable assumptions on the matrix A(x, s), and depending on the behaviour of the function f near u = 0 and near u = +∞, we can use bifurcation theory in order to give a quite complete analysis on the set of positive solutions. We will generalize in different directions some of the results in the papers by Ambrosetti et al., Ambrosetti and Hess, and Artola and Boccardo.

Qualitative Analysis of a Predator–Prey Model with Crowley–Martin Functional Response

2015 ◽  
Vol 25 (09) ◽  
pp. 1550110 ◽  
Author(s):  
Yaying Dong ◽  
Shunli Zhang ◽  
Shanbing Li ◽  
Yanling Li
Keyword(s):  
Functional Response ◽  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Key Parameter

In this paper, we are concerned with positive solutions of a predator–prey model with Crowley–Martin functional response under homogeneous Dirichlet boundary conditions. First, we prove the existence and reveal the structure of the positive solutions by using bifurcation theory. Then, we investigate the uniqueness and stability of the positive solutions for a large key parameter. In addition, we derive some sufficient conditions for the uniqueness of the positive solutions by using some specific inequalities. Moreover, we discuss the extinction and persistence results of time-dependent positive solutions to the system. Finally, we present some numerical simulations to supplement the analytic results in one dimension.

scholarly journals Positive solutions of an asymptotically planar system of elliptic boundary value problems

1998 ◽  
Vol 21 (3) ◽  
pp. 549-554 ◽  
Author(s):  
F. J. S. A. Corrêa
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Bifurcation Theory ◽  
Existence Result ◽  
Elliptic Boundary ◽  
Elliptic Boundary Value Problems ◽  
Planar System ◽  
Elliptic Boundary Value

We will prove an existence result of positive solutions for an asymptotically planar system of two elliptic equations. It will be used as main tools for a Maximum Principle and a result on Bifurcation Theory.

scholarly journals Positive Solutions of a System Arising from Angiogenesis

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Manuel Delgado ◽  
Antonio Suárez
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Bifurcation Theory ◽  
Time Dependent ◽  
System Of Equations ◽  
Time Dependent Problem ◽  
Loss Of Regularity

AbstractWe study a system of equations arising from angiogenesis which contains a non- regular term that vanishes below a certain threshold. We are forced to modify the usual methods of bifurcation theory because of this loss of regularity. Nevertheless, we obtain results on the existence, uniqueness and permanence of a positive solution for the time-dependent problem; and the existence and uniqueness of a positive solution for the stationary one.

On the Structure of Positive Solutions for the Shigesada–Kawasaki–Teramoto Model with Large Interspecific Competition Rate

2020 ◽  
Vol 30 (01) ◽  
pp. 2050001
Author(s):  
Yukio Kan-on
Keyword(s):  
Positive Solution ◽  
Interspecific Competition ◽  
Positive Solutions ◽  
Comparison Principle ◽  
Nonlinear Diffusion ◽  
Bifurcation Theory ◽  
Diffusion System ◽  
Bifurcation Structure ◽  
Diffusion Term ◽  
Competition Diffusion

In this paper, we treat the competition-diffusion system with nonlinear diffusion term, which was proposed by Shigesada et al. [1979], and discuss the bifurcation structure of positive solution for the system when the interspecific competition rate is sufficiently large. To do this, we derive two kinds of limiting systems as the interspecific competition rate tends to infinity, and study the bifurcation structure of positive solution for each limiting system by employing the comparison principle and the bifurcation theory.

scholarly journals AN EIGENVALUE PROBLEM FOR A NON-BOUNDED QUASILINEAR OPERATOR

2004 ◽  
Vol 47 (2) ◽  
pp. 353-363 ◽  
Author(s):  
José Carmona ◽  
Antonio Suárez
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Bifurcation Theory ◽  
Bifurcation Parameter ◽  
Quasilinear Elliptic Problem ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Quasilinear Elliptic ◽  
Range Of Values

AbstractIn this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with an operator that is not necessarily bounded. For that, we use the bifurcation theory and obtain the existence of positive solutions for a range of values of the bifurcation parameter.AMS 2000 Mathematics subject classification: Primary 35J60; 35J25. Secondary 35D05

Multiple coexistence solutions to the unstirred chemostat model with plasmid and toxin

2014 ◽  
Vol 25 (4) ◽  
pp. 481-510 ◽  
Author(s):  
HUA NIE ◽  
JIANHUA WU
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Positive Solutions ◽  
Bifurcation Theory ◽  
Fixed Point Index ◽  
Index Theory ◽  
Point Index ◽  
Chemostat Model ◽  
Fixed Point Index Theory ◽  
Exact Multiplicity

We investigate the effects of toxins on the multiple coexistence solutions of an unstirred chemostat model of competition between plasmid-bearing and plasmid-free organisms when the plasmid-bearing organism produces toxins. It turns out that coexistence solutions to this model are governed by two limiting systems. Based on the analysis of uniqueness and stability of positive solutions to two limiting systems, the exact multiplicity and stability of coexistence solutions of this model are established by means of the combination of the fixed-point index theory, bifurcation theory and perturbation theory.

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