We consider the following coupled Schr$ \ddot{o} $dinger system with critical exponent in $ \mathbb{R}^3: $$ \left \{ \begin{aligned} &-\Delta u+\lambda V(|y|)u = K_1(|y|)u^5+u^2v^3,\qquad &\text{ } \mathbb{R}^3\backslash B_\epsilon(0),\\ v+\lambda V(|y|)v K_2(|y|)v^5+v^2u^3, \qquad &u >0, v>0, \quad B_\epsilon(0), \\ & (u,v) (0,0), &\text{on \partial B_\epsilon (0), &...

Abstract In the present paper, we study existence of normalized solutions for following coupled elliptic system with quadratic nonlinearity − Δ u λ...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

We formulate a hierarchy of models relevant for studying coupled well-reservoir flows. The starting point is an integral equation representing unsteady single-phase 3-D porous media flow and the 1-D isothermal Euler equations representing unsteady well flow. This 2 × 2 system of conservation laws is coupled to the integral equation through natural coupling conditions accounting for the flow bet...

We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...

We consider the controllability of a chemotaxis system of parabolic–elliptic type. By linearizing the nonlinear system into two separate linear equations, we can bypass the obstacle caused by the nonlinear drift term and establish local null controllability of the original nonlinear system. This approach is different from the usual method for dealing with coupled parabolic systems. © 2013 Elsev...

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...

A nonlinear coupled system descriptive of multi-ion electrodiffusion is investigated and all parameters for which the system admits a single-valued general solution are isolated. This is achieved via a method initiated by Painlevé with the application of a test due to Kowalevski and Gambier. The solutions can be obtained explicitly in terms of Painlevé transcendents or elliptic functions.

We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary solution for L 2 initial data. This paper extends and improves on a body of work surrounding the Debye-Hückel system to the hydrodyanamical case.