scholarly journals Existence and Multiplicity of Positive Solutions to a Quasilinear Elliptic Equation with Strong Allee Effect Growth Rate

2013 ◽  
Vol 64 (1-2) ◽  
pp. 165-173 ◽  
Author(s):  
Chan-Gyun Kim ◽  
Junping Shi
Keyword(s):  
Growth Rate ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Quasilinear Elliptic Equation ◽  
Allee Effect ◽  
Existence And Multiplicity ◽  
Strong Allee Effect ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic

scholarly journals Logistic equation with thep-Laplacian and constant yield harvesting

2004 ◽  
Vol 2004 (9) ◽  
pp. 723-727 ◽  
Author(s):  
Shobha Oruganti ◽  
Junping Shi ◽  
Ratnasingham Shivaji
Keyword(s):  
Growth Rate ◽  
Elliptic Equation ◽  
Positive Constant ◽  
Quasilinear Elliptic Equation ◽  
Rate Function ◽  
Logistic Equation ◽  
Solution Methods ◽  
Growth Rate Function ◽  
Quasilinear Elliptic ◽  
Constant Yield

We consider the positive solutions of a quasilinear elliptic equation withp-Laplacian, logistic-type growth rate function, and a constant yield harvesting. We use sub-super-solution methods to prove the existence of a maximal positive solution when the harvesting rate is under a certain positive constant.

scholarly journals Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems

2018 ◽  
Vol 36 (4) ◽  
pp. 197-208
Author(s):  
Khaled Ben Ali ◽  
Abdeljabbar Ghanmi
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Smooth Function ◽  
Smooth Boundary ◽  
Nehari Manifold ◽  
Multiplicity Result ◽  
Existence And Multiplicity ◽  
Open Set ◽  
Multiplicity Of Positive Solutions

This article shows the existence and multiplicity of positive solutions of the $p$-Laplacien problem $$\displaystyle -\Delta_{p} u=\frac{1}{p^{\ast}}\frac{\partial F(x,u)}{\partial u} + \lambda a(x)|u|^{q-2}u \quad \mbox{for } x\in\Omega;\quad \quad u=0,\quad \mbox{for } x\in\partial\Omega$$ where $\Omega$ is a bounded open set in $\mathbb{R}^n$ with smooth boundary, $1<q<p<n$, $p^{\ast}=\frac{np}{n-p}$, $\lambda \in \mathbb{R}\backslash \{0\}$ and $a$ is a smooth function which may change sign in $\overline{\Omega}$. The method is based on Nehari results on three sub-manifolds of the space $W_{0}^{1,p}$.

scholarly journals Existence and multiplicity results for quasilinear elliptic equations

2005 ◽  
Vol 71 (3) ◽  
pp. 377-386 ◽  
Author(s):  
Wei Dong
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Bounded Open Subset ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic ◽  
Laplacian Operators

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

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