Stability and Intersection Properties of Solutions to the Nonlinear Biharmonic Equation
نویسنده
چکیده
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation ∆φ = φ. First, we show that there exists a critical value pc, depending on the space dimension, such that the solutions are linearly unstable if p < pc and linearly stable if p ≥ pc. Then, we focus on the supercritical case p ≥ pc and we show that the graphs of no two solutions intersect one another.
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