Integral equations arising in the kinetic theory of gases. (English) Zbl 0697.45004

The paper contains an existence result for the nonlinear integral equation of the form \((1)\quad x(t)=\psi (t)+[f(t,x(t))+\int^{\infty}_{0}\sigma (t,s)x(s)ds]\int^{\infty}_{0}\sigma (t,s)K(s,x(s))ds.\) The functions involved in (1) are members of the space \(L^ p(R_+)\), \(1\leq p\leq \infty.\)
In the reviewer’s opinion the results obtained in the paper are “almost” trivial because the authors assume the Lipschitz continuity of the functions occurring in the equation (1). Moreover, the text contains several misprints which make the paper to be illegible in general. For example, the assumption \((A_ 2)\) exploits a function h which does not occur in the equation (1).
Reviewer: J.Banaś


45G10 Other nonlinear integral equations
82B40 Kinetic theory of gases in equilibrium statistical mechanics
Full Text: DOI


[1] DOI: 10.1090/S0002-9904-1947-08825-X · Zbl 0031.23603
[2] DOI: 10.1093/qmath/os-18.1.244 · Zbl 0029.26901
[3] DOI: 10.1016/0022-247X(77)90272-4 · Zbl 0352.45004
[4] DOI: 10.1137/0509060 · Zbl 0388.45004
[5] DOI: 10.1016/0022-247X(78)90066-5 · Zbl 0379.45022
[6] Yosida K., Functional Analysis (1978) · Zbl 0365.46001
[7] Darbo G., Rend. Sem. Mat. Univ. Padua 24 pp 84– (1955)
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