Advanced Search
Article Contents
Article Contents

A logistic equation with refuge and nonlocal diffusion

Abstract Related Papers Cited by
  • In this work we consider the nonlocal stationary nonlinear problem $(J* u)(x) - u(x)= -\lambda u(x)+ a(x) u^p(x)$ in a domain $\Omega$, with the Dirichlet boundary condition $u(x)=0$ in $\mathbb{R}^N\setminus \Omega$ and $p>1$. The kernel $J$ involved in the convolution $(J*u) (x) = \int_{\mathbb{R}^N} J(x-y) u(y) dy$ is a smooth, compactly supported nonnegative function with unit integral, while the weight $a(x)$ is assumed to be nonnegative and is allowed to vanish in a smooth subdomain $\Omega_0$ of $\Omega$. Both when $a(x)$ is positive and when it vanishes in a subdomain, we completely discuss the issues of existence and uniqueness of positive solutions, as well as their behavior with respect to the parameter $\lambda$.
    Mathematics Subject Classification: Primary: 45C05, 45M05, 45M20.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(156) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint