Waveform at the switch of a boost converter. What is causing the oscillation when the switch is open?
It looks like a perfectly normal DCM (discontinuous conduction mode) waveform to me.

The lowest, straight segment is when the switch (to ground) inside the LM2588 is conducting, charging the inductor with current.

The next segment, the high straight one, is when the switch has cut off, and the inductor is now dumping its energy into the output capacitor(s) through the diode.

At the end of that segment, the energy in the coil is exhausted &mdash; i.e., its current drops to zero. There is now a reverse bias across the coil, and the current tries to flow in the other direction, but this is blocked by the diode.

Now you have a coil that is open-circuit at one end (neither the LM2588 nor the diode are conducting), but its internal distributed capacitance is charged to Vout - Vin. The next thing you see is the self-resonance of the coil dissipating that energy in the form of a sinewave (superimposed on a DC bias equal to Vin). This waveform decays at a rate determined by the Q (quality factor, or internal resistance) of the coil. This continues to the start of the next switching cycle.

The sinewave part of the cycle represents a relatively tiny amount of energy. However, since it occurs at a single specific frequency, it can be an annoying source of EMI. A damping resistor or an R-C snubber can be used to suppress it if necessary.

The self-resonant frequency seems to have a period of about 1.4 &micro;s (714 kHz). Given this, and the inductance of 390 &micro;H, you can infer that the effective distributed capacitance is about 130 pF.