拟对称packing极小Moran集

本文研究了一维Moran集的拟对称packing极小性的问题.利用质量分布原理的方法,获得了直线上一类packing维数为1的Moran集为拟对称packing极小集的结果,推广了参考文献中关于拟对称packing极小性的已知结果.     

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS

We consider the following nonlinear Schr¨odinger equations -ε2△u + u = Q(x)|u|p-2u in RN, u ∈ H1(RN),where ε is a small positive parameter, N ≥ 2, 2 p ∞ for N = 2 and 2 p 2N/N-2 for N ≥ 3. We prove that this problem has sign-changing(nodal) semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q(x).Moreover, the number of this type of solutions will go to infinity as ε→ 0+.     

一类Kirchhoff-Carrier型方程正规化解的存在性及其性态

本文主要研究Kirchhoff-Carrier型方程■正解的存在性及其性态,其中N≥1,a,b,c,d均为固定的正数,(λ,u)∈R⁺×H¹(R^N).我们利用伸缩技巧证明了上述问题在不同的假设条件下正解的存在性,非存在性和多重性.