## Journal of Integral Equations and Applications

### Constructive Analysis of Purely Integral Boltzmann Models

#### Article information

Source
J. Integral Equations Applications Volume 11, Number 3 (1999), 393-404.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1181074284

Digital Object Identifier
doi:10.1216/jiea/1181074284

Mathematical Reviews number (MathSciNet)
MR1719079

Zentralblatt MATH identifier
0974.45005

#### Citation

Sommariva, Alvise; Vianello, Marco. Constructive Analysis of Purely Integral Boltzmann Models. J. Integral Equations Applications 11 (1999), no. 3, 393--404. doi:10.1216/jiea/1181074284. https://projecteuclid.org/euclid.jiea/1181074284

#### References

• V.C. Boffi and G. Spiga, An equation of Hammerstein type arising in particle transport theory, J. Math. Phys. 24 (1983), 1625-1629.
• V.C. Boffi, R.L. Bowden and G. Spiga, On the solutions to a class of nonlinear integral equations arising in transport theory, J. Math. Phys. 25 (1984), 3444-3450.
• V.C. Boffi, G. Spiga and J.R. Thomas, Jr., Solution of a nonlinear integral equation arising in particle transport theory, J. Comput. Phys. 59 (1985), 96-107.
• C. Cercignani, The Boltzmann equation and its applications, Springer, New York, 1988.
• J. Dieudonné, Foundations of modern analysis, Academic Press, New York, 1969.
• L. Erbe, D. Guo and X. Liu, Positive solutions of a class of nonlinear integral equations and applications, J. Integral Equations Appl. 4 (1992), 179-195.
• G.B. Folland, Real analysis, John Wiley and Sons, New York, 1984.
• D. Guo, Positive fixed points and eigenvectors of noncompact decreasing operators with applications to nonlinear integral equations, Chin. Ann. Math. 4 (1993), 419-426.
• D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones, Academic Press, Inc., New York, 1988.
• R.W. Leggett, A new approach the $H$-equation of Chandrasekhar, SIAM J. Math. Anal. 7 (1976), 542-550.
• M.A. Krasnoselskii, Positive solutions of operator equations, P. Noordhoff, Groningen, 1964.
• A. Sommariva and M. Vianello, Approximating fixed-points of decreasing operators in spaces of continuous functions, Numer. Funct. Anal. Optim. 19 (1998), 635-646.
• --------, Constructive approximation for a class of perturbed Hammerstein integral equations, Nonlinear Anal., in press.
• F.G. Tricomi, Integral equations, Interscience, New York, 1957.