Abstract
We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [0,1) and those solutions are globally attractive.
Highlights
Quadratic integral equations are often applicable in the theory of radiative transfer, kinetic theory of gases, in the theory of neutron transport and in the traffic theory
The so-called quadratic integral equation of Chandrasekhar type can be very often encountered in many applications
In this paper we study the functional integral equation of mixed type, namely t x(t) = f t, x(t), u(t, s, x(s))ds, v(t, s, x(s)) ds
Summary
Quadratic integral equations are often applicable in the theory of radiative transfer, kinetic theory of gases, in the theory of neutron transport and in the traffic theory. The so-called quadratic integral equation of Chandrasekhar type can be very often encountered in many applications (cf [1, 2, 3, 6, 7, 8, 9, 10, 13, 14]). In this paper we study the functional integral equation of mixed type, namely t. Eq(1) contains as special cases numerous integral and functional-integral equations encountered in nonlinear analysis. The famous Chandrasekhar’s integral equation is considered as a special case. Our result in this paper is motivated by the extension of the work of Hu and Yan [12]
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