We consider the following system of Liouville equations: âÎu1=2eu1+μeu2in R2âÎu2=μeu1+2eu2in R2â«R2eu1<+â,â«R2eu2<+â. We show the existence of at least nâ[n3] global branches of nonradial solutions bifurcating from u1(x)=u2(x)=U(x)=logâ¡64(2+μ)(8+|x|2)2 at the values μ=â2n2+nâ2n2+n+2 for any nâN.
Battaglia, L., Gladiali, F., Grossi, M. (2017). Nonradial entire solutions for Liouville systems. JOURNAL OF DIFFERENTIAL EQUATIONS, 263(8), 5151-5174 [10.1016/j.jde.2017.06.009].
Nonradial entire solutions for Liouville systems
Battaglia, Luca;GROSSI, Massimo
2017-01-01
Abstract
We consider the following system of Liouville equations: âÎu1=2eu1+μeu2in R2âÎu2=μeu1+2eu2in R2â«R2eu1<+â,â«R2eu2<+â. We show the existence of at least nâ[n3] global branches of nonradial solutions bifurcating from u1(x)=u2(x)=U(x)=logâ¡64(2+μ)(8+|x|2)2 at the values μ=â2n2+nâ2n2+n+2 for any nâN.File in questo prodotto:
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