Vol. 41, No. 3, 1972

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On multidimensional integral equations of Volterra type

Manda Butchi Suryanarayana

Vol. 41 (1972), No. 3, 809–828

It is the purpose of this paper to study multidimensional nonlinear integral equations of Volterra type of a rather general form with unknowns in one of the function spaces C,L1,L or Lp,1 < p < +. In analogy with the theory of differential equations, global existence and uniqueness theorems as well as continuous dependence on initial values, are established for such integral equations. The hypotheses on integrands in this paper are less demanding than normally found in the literature and are motivated by applications, particularly to boundary value problems found in optimal control theory.

Mathematical Subject Classification 2000
Primary: 45D05
Received: 7 January 1971
Published: 1 June 1972
Manda Butchi Suryanarayana