Entire Solutions of

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...

Entire Invariant Solutions to Monge-ampère Equations

We prove existence and regularity of entire solutions to MongeAmpère equations invariant under an irreducible action of a compact Lie group. We consider Monge-Ampère equations of the form f(∇φ) detDijφ = g(x) (0.1) where f and g are nonnegative measurable functions on R. We recall first the concept of a weak solution of (0.1). Let φ be a convex function. Then ∇φ is a well-defined multi-valued m...

Radial entire solutions for supercritical biharmonic equations ∗

We prove existence and uniqueness (up to rescaling) of positive radial entire solutions of supercritical semilinear biharmonic equations. The proof is performed with a shooting method which uses the value of the second derivative at the origin as a parameter. This method also enables us to find finite time blow up solutions. Finally, we study the convergence at infinity of regular solutions tow...