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

Hu, Shouchouan; Khavanin, Mohamed; Zhuang, Wan

Appl. Anal. 34, No. 3-4, 261-266 (1989).

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

MSC:

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

Keywords:

nonlinear integral equation

References:

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