Vitali Vougalter
Solvability of some quadratic integral equations in higher dimensions
(164K, pdf)

ABSTRACT.  The work deals with the existence of solutions of a certain quadratic integral equation in H^3(R^d), d=4,5. The theory of quadratic integral equations has many significant applications in the mathematical physics, economics, biology. It is important for describing the real world problems. The proof of the existence of solutions is based on a fixed point technique in the Sobolev space in dimensions four and five.