## Differential and Integral Equations

### Existence results for some functional elliptic equations

#### Abstract

We consider nonlocal elliptic boundary value problems of the form $$-\mathcal{A}(x,u) \bigtriangleup u = \lambda f(u)$$ with Dirichlet boundary conditions. We show that if $f$ has $n$ loops, then the problem has at least $n$ distinct solutions, by using very simple comparison principles. Also, we study the asymptotic behavior of such solutions as the parameter $\lambda$ tends to $\infty$.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 289-300.

Dates
First available in Project Euclid: 30 January 2014