showing 2 related works from this author
Parabolic equations with natural growth approximated by nonlocal equations
2017
In this paper we study several aspects related with solutions of nonlocal problems whose prototype is $$ u_t =\displaystyle \int_{\mathbb{R}^N} J(x-y) \big( u(y,t) -u(x,t) \big) \mathcal G\big( u(y,t) -u(x,t) \big) dy \qquad \mbox{ in } \, \Omega \times (0,T)\,, $$ being $ u (x,t)=0 \mbox{ in } (\mathbb{R}^N\setminus \Omega )\times (0,T)\,$ and $ u(x,0)=u_0 (x) \mbox{ in } \Omega$. We take, as the most important instance, $\mathcal G (s) \sim 1+ \frac{\mu}{2} \frac{s}{1+\mu^2 s^2 }$ with $\mu\in \mathbb{R}$ as well as $u_0 \in L^1 (\Omega)$, $J$ is a smooth symmetric function with compact support and $\Omega$ is either a bounded smooth subset of $\mathbb{R}^N$, with nonlocal Dirichlet bound…
Quasilinear elliptic equations with singular quadratic growth terms
2011
In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.