Continuous dependence for p-Laplace equations with varying operators
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.13674
- arXiv:
- arXiv:2405.13674
- Bibcode:
- 2024arXiv240513674C
- Keywords:
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- Mathematics - Analysis of PDEs