TY - JOUR
T1 - Unique solvability of nonlinear Volterra equations in weighted spaces
AU - Rejto, Peter
AU - Taboada, Mario
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1992/7/1
Y1 - 1992/7/1
N2 - We investigate integral equations of the form x(t) = g(t) + ∫-∞t F(t, s, x(s)) ds. (*) In general, this equation is history-dependent, so one needs to give an initial condition on (-∞, 0] in order to obtain a unique solution. By introducing a weight function on R, we can single out a class of admissible solutions, and give conditions for the unique solvability of (*) in this restricted class. We also study some Fredholm equations on these weighted spaces. In addition, we also treat a class of equations of the first kind for which similar conclusions can be drawn.
AB - We investigate integral equations of the form x(t) = g(t) + ∫-∞t F(t, s, x(s)) ds. (*) In general, this equation is history-dependent, so one needs to give an initial condition on (-∞, 0] in order to obtain a unique solution. By introducing a weight function on R, we can single out a class of admissible solutions, and give conditions for the unique solvability of (*) in this restricted class. We also study some Fredholm equations on these weighted spaces. In addition, we also treat a class of equations of the first kind for which similar conclusions can be drawn.
UR - https://www.scopus.com/pages/publications/38249012296
UR - https://www.scopus.com/pages/publications/38249012296#tab=citedBy
U2 - 10.1016/0022-247X(92)90213-W
DO - 10.1016/0022-247X(92)90213-W
M3 - Article
AN - SCOPUS:38249012296
SN - 0022-247X
VL - 167
SP - 368
EP - 381
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -