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

Volume 27 / 2000

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


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.


  • Tadeusz Nadzieja
  • Andrzej Raczyński

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