We consider the following coupled elliptic system :  −∆u = μ1u N+2 N−2 + βu 2 N−2 v N N−2 in R −∆v = μ2v N+2 N−2 + βv 2 N−2u N N−2 in R u, v > 0, u, v ∈ D(R ), (S) where N = 3, 4, μ1, μ2 are two positive constants and β < 0 is the coupling constant. We prove the existence of infinitely many positive nonradial solutions.

This paper is concerned with a cooperative two-species Lotka–Volterra model. Using the fixed point theorem, the existence results of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions are obtained. Our results show that this model possesses at least one coexistence state if the birth rates are big and cross-diffusions are suitably weak. c © 2007 Elsev...

Consider the N -coupled nonlinear elliptic system (P) >< >: −∆Uj + Uj = μU j + βUj X k 6=j U k in Ω, Uj > 0 in Ω, Uj = 0 on ∂Ω, j = 1, . . . , N. where Ω is a smooth and bounded (or unbounded if Ω is radially symmetric) domain in Rn, n ≤ 3. By using a ZN index theory, we prove the existence of multiple solutions of (P) and show the dependence of multiplicity results on the coupling constant β.

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

The linear systems that are most amenable to solution by iterative methods are those that come from discretisation of partial differential equations, in particular those from mathematical physics. Here are a few of the possible sources of linear systems: • Elliptic equations. These always give a linear system to solve. One characteristic1 of elliptic systems is that all points of the solution a...

A new model for distributed capacitance in a conducting medium is introduced as a system of local RC diiusion equations coupled by a global elliptic equation. This model contains the local geometry of the distributed capacitors on which charge is stored and the exchange of current ux on their interface with the medium. The resulting degenerate initial-boundary-value problem is shown to be well ...

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function Σ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of Σ in the sense of subdifferential calcul...

An autonomous system of three coupled nonlinear oscillators with widely separated frequencies is investigated using the method of direct partition of motion (DPM). Approximate expressions for two of the limit cycle oscillations are presented in terms of Jacobi elliptic functions whose amplitude and frequency depend on the coupling parameters. Critical values for the coupling parameters were fou...