# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

### Tom 27 / 2000

Applicationes Mathematicae 27 (2000), 465-473 DOI: 10.4064/am-27-4-465-473

#### Streszczenie

We consider the following problem: $ΔΦ = ± {M οver \int_{Ω} e^{- Φ/Θ}} e^{- Φ/Θ}, E = MΘ ∓ {1οver2}\int_{Ω} |∇Φ|^2, Φ|_{\partial Ω} = 0,$ where Φ: Ω ⊂ $ℝ^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.