Article Contents
Article Contents

# Multiple stable patterns for some reaction-diffusion equation in disrupted environments

• We study the existence of multiple positive stable solutions for

$-\epsilon^2\Delta u(x) = u(x)^2(b(x)-u(x)) \ \mbox{in}\ \Omega, \quad$ $\frac{\partial u}{\partial n}(x) = 0 \ \mbox{on}\ \partial\Omega.$

Here $\epsilon>0$ is a small parameter and $b(x)$ is a piecewise continuous function which changes sign. These type of equations appear in a population growth model of species with a saturation effect in biology.

Mathematics Subject Classification: Primary 35J65, 35B05, 58E05; Secondary: 92C15.

 Citation: