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arXiv · 2405.13674

Continuous dependence for p-Laplace equations with varying operators

Francesca Colasuonno·Benedetta Noris·Elisa Sovrano
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Abstract

For the following Neumann problem in a ball $$\begin{cases} -\Delta_p u+u^{p-1}=u^{q-1}\quad&\text{in }B,\\ u>0,\,u\text{ radial}\quad&\text{in }B,\\ \frac{\partial u}{\partial \nu}=0\quad&\text{on }\partial B, \end{cases}$$ 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.

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Francesca Colasuonno, Benedetta Noris, Elisa Sovrano. 2024-05-22. Continuous dependence for p-Laplace equations with varying operators. https://arxiv.org/abs/2405.13674

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