Continuous dependence for $ p $ -Laplace equations with varying operators
Francesca Colasuonno, Benedetta Noris, Elisa Sovrano · Discrete and Continuous Dynamical Systems - S · 2024
For the following Neumann problem in a ball$ \begin{cases} -\Delta_p u+u^{p-1} = u^{q-1}\quad&\mbox{in }B,\\ u>0,\,u\mbox{ radial}\quad&\mbox{in }B,\\ \dfrac{\partial u}{\partial u} = 0\quad&\mbox{on }\partial B, \end{cases} $with $ 1<p<q<\infty $, we prove continuous dependence on $ p $, for radially nondecreasing solutions. As a byproduct, we obtain an existence result for nonconstant solutions in the case $ p\in(1,2) $ and $ q $ larger than an explicit threshold.