Nonexistence of nonnegative entire solutions of semilinear elliptic systems

On the existence and nonexistence of positive entire large solutions for semilinear elliptic equations

In this paper we are studying the existence of positive entire large solutions for the problem ∆u = p1(x)u α + p2(x)u f(u) in R , N ≥ 3. Moreover, we are interested in the relation between the existence or nonexistence of such solutions for the above problem and the existence or nonexistence of such solutions for the problems ∆u = p1(x)u α and ∆u = p2(x)u f(u).

Asymptotic Spatial Patterns and Entire Solutions of Semilinear Elliptic Equations

(2) ε∆uε + f(uε) = 0, x ∈ Ω, Bu = 0, x ∈ ∂Ω, where ε > 0 is a small parameter, Ω is a smooth bounded domain in Rn, and Bu is an appropriate boundary condition. The connection of (1) and (2) are made by a typical technique called blowup method. Suppose that {uε} is a family of solutions of (2). The simplest setup of the blowup method is to choose Pε ∈ Ω, and define vε(y) = uε(εy + Pε), for y ∈ Ω...

Nonexistence and Radial Symmetry of Positive Solutions of Semilinear Elliptic Systems

Existence and Nonexistence of Entire Solutions for Non-cooperative Cubic Elliptic Systems

In this paper we deal with the cubic Schrödinger system −∆ui = n ∑ j=1 βiju 2 jui, u1, . . . , un ≥ 0 in R N (N ≤ 3), where β = (βi,j)ij is a symmetric matrix with real coefficients and βii ≥ 0 for every i = 1, . . . , n. We analyse the existence and nonexistence of nontrivial solutions in connection with the properties of the matrix β, and provide a complete characterization in dimensions N = ...

Existence of Entire Positive Solutions for a Class of Semilinear Elliptic Systems

Under simple conditions on fi and gi, we show the existence of entire positive radial solutions for the semilinear elliptic system ∆u = p(|x|)f1(v)f2(u) ∆v = q(|x|)g1(v)g2(u), where x ∈ RN , N ≥ 3, and p, q are continuous functions.