By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where drift contains term growing linearly space locally integrable independent of distribution, while noise coefficient is weakly differentiable Lipschitz continuous respect to sum Wasserst...

In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to establish the global existence and uniqueness for fractional differential equations of Riemann–Liouville type. Some examples provided illustrate applicability our main results.

Keywords: Integro-differential equations Volterra equations Abel's integral equations Bernstein polynomials Singular volterra integral equations a b s t r a c t In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of a class of linear Volterra integro-differential equations with weakly singular kernel. If the exact solution is pol...

We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Isin...

Let Ω ⊂ Ω̃ be open sets in R, I ⊂ R be an open neighborhood of the origin and let η be a compactly supported smooth function on Ω× I; we assume that η(·, 0) does not vanish identically. For each x ∈ Ω let t 7→ Γ(x, t) ⊂ Ω̃ be a regular parametrization of a submanifold Mx ⊂ Ω̃ with codimension l. We assume that Γ(x, t) ⊂ Ω if (x, t) ∈ supp η, and that Γ satisfies Γ(x, 0) = x and depends smoothly on...