Tiancheng Ouyang

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where B” is the unit ball in R”. )I 2 I. and I. is a positive parameter. It is well known that iffis a smooth function, then any positive solution to the equation is radially symmetric, and all solutions can be pdrameterized by their maximum values. We develop a unitied approach to obtain the exact multiplicity of the positive solutions for a wide class ol’(More)
Analytical methods are used to prove the existence of a periodic, symmetric solution in the 4-body problem with singularities. A numerical calculation and simulation are used to generate the orbit. The analytical method easily extends to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated.