带参数的渐近线性椭圆方程组解的分歧性

利用Lyapunov-Schmidt约化方法结合Rabinowitz大范围分歧理论,研究了一类带有参数的渐近线性椭圆方程组正、负解的存在性以及分歧性。首先给出了由正、负解所组成的连续统在分歧点附近的存在性,结合非线性项的合理假设,进而给出了连续统在分歧点附近沿着λ方向的分歧性态。

Bifurcation of solutions of a class of asymptotically linear elliptic systems with parameters

Graphene oxide was prepared by modified Hummers method and then treated by chemical Cu plating. The composites consisted of pure Al as matrix and Cu-coated graphene oxide as reinforcing phase. The Cu-coated graphene Al-based composites with different mass fraction were prepared by spark plasma sintering. The microstructures of composites were characterized by scanning electron microscope (SEM) and X-ray diffractometer (XRD). The mechanical properties of composites were tested by micro-tensile apparatus. The results show that when the mass fraction of Cu-coated graphene reaches 0.15%, Cu-coated graphene Al-matrix composites exhibit the best comprehensive properties. The Vickers hardness and tensile strength are 56 and 224 MPa, which are 6% and 24% higher than those of graphene Al-matrix composite, and 30% and 103% higher than those of pure Al. The Cu-coated graphene Al-matrix composite have better antifriction performance.