Asymptotic behaviour of positive solutions of periodic delay logistic equations

1982 ◽  
Vol 14 (1) ◽  
pp. 95-100 ◽  
Author(s):  
M. Badii ◽  
A. Schiaffino
Keyword(s):  
Asymptotic Behaviour ◽  
Positive Solutions ◽  
Logistic Equations ◽  
Periodic Delay

Positive Solutions for the Generalized Nonlinear Logistic Equations

2016 ◽  
Vol 59 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Type Result ◽  
Logistic Equations ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiòusive type. Using variationalmethods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers

2021 ◽  
pp. 1-18
Author(s):  
Lucio Boccardo ◽  
Liliane Maia ◽  
Benedetta Pellacci
Keyword(s):  
Linear Operator ◽  
Asymptotic Behaviour ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Existence Results ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Image Position

We prove existence results of two solutions of the problem \[ \begin{cases} L(u)+u^{m-1}=\lambda u^{p-1} & \text{in}\ \Omega,\\ u>0 & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial \Omega, \end{cases} \] where $L(v)=-\textrm {div}(M(x)\nabla v)$ is a linear operator, $p\in (2,2^{*}]$ and $\lambda$ and $m$ sufficiently large. Then their asymptotical limit as $m\to +\infty$ is investigated showing different behaviours.

A variational approach to nonlinear logistic equations

2015 ◽  
Vol 17 (03) ◽  
pp. 1450021 ◽  
Author(s):  
Leszek Gasiński ◽  
Donal O'Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Positive Solutions ◽  
Variational Approach ◽  
Continuous Dependence ◽  
Type Equation ◽  
Logistic Equation ◽  
Extremal Solutions ◽  
Constant Sign ◽  
Nontrivial Solutions ◽  
Logistic Equations ◽  
Solutions Of Constant Sign

We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of constant sign and in fact we establish the existence of extremal constant sign solutions. Using these extremal solutions, we produce a nodal (sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

Asymptotic behaviour of solutions to abstract logistic equations

2007 ◽  
Vol 206 (2) ◽  
pp. 216-232 ◽  
Author(s):  
Janet Dyson ◽  
Rosanna Villella-Bressan ◽  
Glenn F. Webb
Keyword(s):  
Asymptotic Behaviour ◽  
Logistic Equations ◽  
Asymptotic Behaviour Of Solutions
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