We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t,x(t)) + B(t,x(a(t))) + f(t)dt = (C(t,x(b(t)) + g(t))dwt, where A(t,·), B(t,·) and C(t,·) are suitable families of non linear operators in Hilbert spaces, wt is a Hilbert valued Wiener process, and a, b are functions of delay. If A satisfies a coercivity condition and a monotonicity hypothesis, and if B, C are Lipschitz continuous, we prove that there exists a unique solution of an initial value problem for the precedent equation. Some examples of interest for the applications are given to illustrate the results.
@article{urn:eudml:doc:42448,
title = {Existence and uniqueness of solutions for non-linear stochastic partial differential equations.},
journal = {Collectanea Mathematica},
volume = {42},
year = {1991},
pages = {51-74},
zbl = {0764.60057},
mrnumber = {MR1181062},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42448}
}
Caraballo Garrido, Tomás. Existence and uniqueness of solutions for non-linear stochastic partial differential equations.. Collectanea Mathematica, Tome 42 (1991) pp. 51-74. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42448/