© Hindawi Publishing Corp. FREDHOLM-VOLTERRA INTEGRAL EQUATION WITH POTENTIAL KERNEL

Abstract. A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T),Ω = {(x,y): x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T]. Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established in the paper. 2000 Mathematics Subject Classification. 45B05, 45D05, 45E10