## Differential and Integral Equations

### Multiple positive solutions for the $m$-Laplacian and a nonlinearity with many zeros

#### Abstract

In this paper, we consider the quasilinear elliptic equation $-\Delta_m u=\lambda f(u)$, in a bounded, smooth and convex domain. When the nonnegative nonlinearity $f$ has multiple positive zeros, we prove the existence of at least two positive solutions for each of these zeros, for $\lambda$ large, without any hypothesis on the behavior at infinity of $f$. We also prove a result concerning the behavior of the solutions as $\lambda\to\infty$.

#### Article information

Source
Differential Integral Equations, Volume 30, Number 1/2 (2017), 145-159.

Dates
First available in Project Euclid: 20 January 2017

Iturriaga, Leonelo; Lorca, Sebastián; Massa, Eugenio. Multiple positive solutions for the $m$-Laplacian and a nonlinearity with many zeros. Differential Integral Equations 30 (2017), no. 1/2, 145--159. https://projecteuclid.org/euclid.die/1484881224