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

Tadeusz Nadzieja; Andrzej Raczyński

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 4, page 465-473
- ISSN: 1233-7234

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topNadzieja, Tadeusz, and Raczyński, Andrzej. "Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy." Applicationes Mathematicae 27.4 (2000): 465-473. <http://eudml.org/doc/219289>.

@article{Nadzieja2000,

abstract = {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.},

author = {Nadzieja, Tadeusz, Raczyński, Andrzej},

journal = {Applicationes Mathematicae},

keywords = {nonlinear elliptic problem; Poisson-Boltzmann equation},

language = {eng},

number = {4},

pages = {465-473},

title = {Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy},

url = {http://eudml.org/doc/219289},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Nadzieja, Tadeusz

AU - Raczyński, Andrzej

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

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 4

SP - 465

EP - 473

AB - 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.

LA - eng

KW - nonlinear elliptic problem; Poisson-Boltzmann equation

UR - http://eudml.org/doc/219289

ER -

## References

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- [5] M. Grüter and K.-O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342. Zbl0485.35031
- [6] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Appl. Math. (Warsaw) 21 (1991), 365-272. Zbl0756.35029
- [7] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. Zbl0777.35001
- [8] R. F. Streater, A gas of Brownian particles in stochastic dynamics, J. Statist. Phys. 88 (1997), 447-469. Zbl0939.82026

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