Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy Tadeusz Nadzieja, Andrzej Raczyński (2000) Applicationes Mathematicae We consider the following problem: Δ Φ = ± M ο v e r ∫ Ω e - Φ / Θ e - Φ / Θ , E = M Θ ∓ 1 ο v e r 2 ∫ Ω | ∇ Φ | 2 , Φ | ∂ Ω = 0 , where Φ: Ω ⊂ ℝ n → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.