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

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Title

Authors ¹, ²

Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

We consider the following problem:

Δ Φ = \pm {M ο v e r \int_{Ω} e^{- \frac{Φ}{Θ}}} e^{- \frac{Φ}{Θ}}, E = M Θ \mp {1 ο v e r 2} \int_{Ω} {| \nabla 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.

nonlinear elliptic problem, Poisson-Boltzmann equation

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