Minimal Energy Solutions and Infinitely Many Bifurcating Branches for a Class of Saturated Nonlinear Schrodinger Systems

作者：Mandel Rainer^*

来源：Advanced Nonlinear Studies, 2016, 16(1): 95-113.

DOI：10.1515/ans-2015-5022

• Nonlinear Schrodinger System with Saturation
• Bifurcation
• Ground States

We prove a conjecture recently formulated by Maia, Montefusco and Pellacci saying that minimal energy solutions of the saturated nonlinear Schrodinger system
{-Delta u + lambda(1)u = alpha u(alpha u(2) + beta v(2))/1 + s(alpha u(2) + beta v(2)) in R-n,
{-Delta v + lambda(2)v = beta v(alpha u(2) + beta v(2))/1 + s(alpha u(2) + beta v(2)) in R-n
are necessarily semitrivial whenever alpha, beta, lambda(1), lambda(2) > 0 and 0 < s < max{alpha/lambda(1), beta/lambda(2)} except for the symmetric case lambda(1) = lambda(2), alpha = beta. Moreover, it is shown that for most parameter samples alpha, beta, lambda(1), lambda(2), there are infinitely many branches containing seminodal solutions which bifurcate from a semitrivial solution curve parametrized by s.

• 出版日期2016-2