We consider the following system of Liouville equations:
⎩⎨⎧−Δu1=2eu1+μeu2−Δu2=μeu1+2eu2∫R2eu1<+∞,∫R2eu2<+∞in R2in R2 We
show existence of at least n−[3n] global branches of
nonradial solutions bifurcating from
u1(x)=u2(x)=U(x)=log(2+μ)(8+∣x∣2)264 at the values
μ=−2n2+n+2n2+n−2 for any n∈N.Comment: 18 pages, accepted on Journal of Differential Equation
In this paper we consider the problem {ll} -\Delta
u=(N+\a)(N-2)|x|^{\a}u^\frac{N+2+2\a}{N-2} & in R^N u>0& in R^N u\in
D^{1,2}(R^N). where N≥3. From the characterization of the solutions of
the linearized operator, we deduce the existence of nonradial solutions which
bifurcate from the radial one when α is an even integer
We study the following generalized SU(3) Toda System
\left\{\begin{array}{ll} -\Delta u=2e^u+\mu e^v & \hbox{ in }\R^2\\ -\Delta
v=2e^v+\mu e^u & \hbox{ in }\R^2\\ \int_{\R^2}e^u<+\infty,\
\int_{\R^2}e^v-2.Weprovetheexistenceofradialsolutionsbifurcatingfromtheradialsolution(\log
\frac{64}{(2+\mu) (8+|x|^2)^2}, \log \frac{64}{ (2+\mu) (8+|x|^2)^2})atthevalues\mu=\mu_n=2\frac{2-n-n^2}{2+n+n^2},\ n\in\N $