Breaking of resonance for elliptic problems with strong degeneration at infinity
Francesco Della Pietra, Ireneo Peral · Communications on Pure & Applied Analysis · 2011
In this paper we study the problem-div$(\frac{Du}{(1+u)^\theta})+|Du|^q =\lambda g(x)u +f$ in $\Omega,$$u=0$ on $\partial \Omega, $$u\geq 0$ in $\Omega,$where $\Omega$ is a bounded open set of $R^n$, $1 0$.The main feature is to show that even for large values of $\theta$there is solution for all $\lambda>0$. The problem could be seen as a reaction-diffusion model which produces a saturation effect,that is, the diffusion goes to zero when $u$ go to infinity.