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arXiv · 0707.3450

Stability and intersection properties of solutions to the nonlinear biharmonic equation

Paschalis Karageorgis
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Abstract

We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation $Δ^2 ϕ= ϕ^p$. First, we show that there exists a critical value $p_c$, depending on the space dimension, such that the solutions are linearly unstable if $p<p_c$ and linearly stable if $p\geq p_c$. Then, we focus on the supercritical case $p\geq p_c$ and we show that the graphs of no two solutions intersect one another.

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Paschalis Karageorgis. 2007-07-23. Stability and intersection properties of solutions to the nonlinear biharmonic equation. https://arxiv.org/abs/0707.3450

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