In this paper, the existence of solutions to a class of non-standard sweeping processes of the form ?u 0 (t) 2 @ C(t) (Au(t)) is established. In contrast to the \classical" sweeping process with A = id, these problems may be degenerated, since there might be no solutions at all.

Sufficient conditions are given, under which the equation y = f(t, y, y′, . . . , y(l))g(y(n−1)) has a singular solution y [T, τ) → R, τ < ∞ satisfying lim t→τ− y(t) = ci ∈ R, i = 0, 1, . . . , l and lim t→τ− |y(j)(t)| = ∞ for j = l + 1, . . . , n− 1 where l ∈ {0, 1, . . . , n− 2}. 2000 Mathematics Subject Classification: 34C11.

In this paper, we consider a corrosion model of iron based alloy in nuclear waste repository. It consists in a PDE system, similar to the steady-state drift-diffusion system arising in semiconductors modelling. The main difference lies in the boundary conditions since they are Robin boundary conditions and infer an additional coupling between the equations. Using a priori estimates on the solut...

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...