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 $\lambda\to\infty$.
Citation
Leonelo Iturriaga. Sebastián Lorca. Eugenio Massa. "Multiple positive solutions for the $m$-Laplacian and a nonlinearity with many zeros." Differential Integral Equations 30 (1/2) 145 - 159, January/February 2017. https://doi.org/10.57262/die/1484881224