Multidimensional entire solutions for an elliptic system modelling phase separation

On Entire Solutions of an Elliptic System Modeling Phase Separations

We study the qualitative properties of a limiting elliptic system arising in phase separation for Bose-Einstein condensates with multiple states:    ∆u = uv in R, ∆v = vu in R, u, v > 0 in R. When n = 1, we prove uniqueness of the one-dimensional profile. In dimension 2, we prove that stable solutions with linear growth must be one-dimensional. Then we construct entire solutions in R with ...

Infinitely Many Entire Solutions of an Elliptic System with Symmetry

Remarks on entire solutions for two fourth order elliptic problems

We are interested in entire solutions for the semilinear biharmonic equation ∆u = f(u) in R , where f(u) = e or −u−p (p > 0). For the exponential case, we prove that for the polyharmonic problem ∆u = e with positive integer m, any classical entire solution verifies ∆2m−1u < 0, this completes the results in [6, 14]; we obtain also a refined asymptotic expansion of radial separatrix solution to ∆...

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

A Remark on Entire Explosive Solutions for a Class of Elliptic System with Linear Gradient Terms

In this paper, we study the existence of positive entire large radial solutions to the nonlinear elliptic system with gradient terms { div(|∇u|p−2∇u) + |∇u| = m(|x|)f1(v)f2(u), x ∈ RN div(|∇v|q−2∇v) + |∇v| = n(|x|)g1(v)g2(u), x ∈ RN (1) The nonlinearities fi, gi (i = 1, 2) are positive and continuous, while the potentials m, n are continuous and certain growth condition. We give some simple con...