On entire solutions of $f^{2}(z)+cf'(z)=h(z)$

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 ...

Entire Solutions of a Fully Nonlinear Equation

Entire solutions of nonlinear differential-difference equations

In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

Entire solutions of the spruce budworm model

Here N is the spruce budworm population density, rB is the linear birth rate of the budworm and KB is the carrying capacity which is related to the density of foliage available on the trees. The P(N)-term represents predation, generally by birds. To be specific, we take the form for P(N) suggested by Ludwig et al., namely BN2 A2+N2 , where A and B are positive constants, and the dynamics of N(t...

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 ∆...