Nonlinear functional differential equations of monotone-type in Hilbert spaces

STOCHASTIC EVOLUUTION EQUATIONS WITH MONOTONE NONLINEARITY IN <em>L^p</em> SPACES

“…In fact, existence and measurability of the solution of (4.1) is necessary in each step of iteration. We proceed as in [15] and we use the method based on random fixed point theory.…”

“…Hamedani and Zangeneh [10] considered a stopped version of monotone-type equations and obtained the existence, uniqueness and measurability of the solutions. Using the tools of random fixed point theory, Jahanipur [15,16,17] generalized this approach to study stochastic functional evolution equations. Moreover, Salavati and Zangeneh [28,30] extended this method to investigate semilinear SEE's with Lévy (jump) noise.…”

“…This is a pathwise inequality for powers r ≥ 2 of stochastic convolution integrals in L p (R), 2 ≤ p < ∞, and generalizes corresponding inequalities (for example, Theorem 2 of [13]). We adopt the same approach as in [15] and we use a method based on random fixed point theory.…”

Fractional neutral stochastic differential equations driven by α-stable process

“…Systems are often subjected to random perturbations. Stochastic differential equations have been investigated by many authors due to playing a very important role in formulation and analysis of many phenomena in economic and finance, physics, mechanics, electric and control engineering, see, for example, Da Prato and Zabczyk [5], Liu [15], Luo and Liu [17], Jahanipur [8], and references therein. Subsequently, with the help of semigroup theory and fractional calculus technique, some authors have also considered fractional stochastic differential equations driven by Brownian motion.…”