On a general SU(3) Toda system

Abstract

We study the following generalized SU (3) Toda Systemwhere μ > −2. We prove the existence of radial solutions bifurcating from the radial solution (log 64 (2+μ)(8+|x| 2 ) 2 , log 64 (2+μ)(8+|x| 2 ) 2 ) at the values μ = μ n = 2 2−n−n 2 2+n+n 2 , n ∈ N.

Nonradial entire solutions for Liouville systems

“…Now let us prove (1.11 Proof of Corollary 1.4. By Theorem 1.1 we get the existence of n − n 3 nonradial nonequivalent solutions and in [4] we got the existence of a radial solution bifurcating by (µ n , U µn , U µn ). So the claim follows.…”

“…and a corresponding (2n + 4)-dimensional kernel. This kernel reduces to a 1-dimensional one if we restrict to the space of the radial function (once we overcome the degeneracy due to the scaling invariance) and this was one of the ideas in [4] to get branches of radial solutions bifurcating by (U µ , U µ ). In order to get a one-dimensional nonradial kernel the argument is more subtle.…”

“…The global bifurcation result in Theorem 1.1 is new also in the case of radial solutions. In the paper [4] only a local radial bifurcation result was proved for system (1.1). Further in the radial setting we can separate the branches getting the following result:…”

Non-uniqueness of blowing-up solutions to the Gelfand problem

“…extended by continuity in s = 1; for details about the formula above, see for instance [18], Lemma 2.1 and [21], Lemma 3.5. As s goes to +∞, one has…”

The asymptotic behavior of Chern–Simons Vortices for Gudnason Model

“…In order to obtain the existence result, they applied a minimization approach. For the recent developments of (1.1), we refer the readers to [15,19,20,23,30,35,37,38,44,53,61,73].…”