In this paper, we study the existence and uniqueness of mild solutions for random impulsive differential equations through fixed point technique. An example is provided to illustrate theory.

This paper concerns with existence, uniqueness and asymptotic behavior of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is pr...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the incompressible Euler equations. Meanwhile, a general technique to prove uniqueness of sufficiently smooth solutions to non-linearly coupled system is introduced,...

We consider a system of n-th order nonlinear quasilinear partial differential equations of the form ut + P(∂ j x)u + g ( x, t, {∂ xu} ) = 0; u(x, 0) = uI(x) with u ∈ C, for t ∈ (0, T ) and large |x| in a poly-sector S in C (∂ x ≡ ∂ j1 x1∂ j2 x2 ...∂ jd xd and j1 + ... + jd ≤ n). The principal part of the constant coefficient n-th order differential operator P is subject to a cone condition. The...

In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...

In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 o...