Multiple Positive Solutions for P-laplacian Equation with Weak Allee Effect Growth Rate
نویسندگان
چکیده
A p-Laplacian equation with weak Allee effect growth rate and Dirichlet boundary condition is considered. The existence, multiplicity and bifurcation of positive solutions are proved with comparison and variational techniques. The existence of multiple positive solutions implies that the related ecological system may exhibit bistable dynamics.
منابع مشابه
Existence and Multiplicity of Positive Solutions to a Quasilinear Elliptic Equation with Strong Allee Effect Growth Rate
In this paper we consider a p-Laplacian equation with strong Allee effect growth rate and Dirichlet boundary condition { div(|∇u|p−2∇u) + λf(x, u) = 0, x ∈ Ω, u = 0, x ∈ ∂Ω, (Pλ) where Ω is a bounded smooth domain in R for N ≥ 1, p > 1, and λ is a positive parameter. By using variational methods and a suitable truncation technique, we prove that problem (Pλ) has at least two positive solutions ...
متن کاملThe fibering map approach to a quasilinear degenerate p(x)-Laplacian equation
By considering a degenerate $p(x)-$Laplacian equation, a generalized compact embedding in weighted variable exponent Sobolev space is presented. Multiplicity of positive solutions are discussed by applying fibering map approach for the corresponding Nehari manifold.
متن کاملAn existence results on positive solutions for a reaction-diffusion model with logistics growth and indefinite weight
In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...
متن کاملPersistence in reaction diffusion models with weak allee effect.
We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak allele effect type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained. Results are applie...
متن کاملTriple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian
In this paper, we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly. Our results ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013