LC Oscillator, Tank Circuit
Providing positive feedback increases the gain of amplifier. Even noises in the atmosphere will be significantly amplified and fed back. 

The circuit given by OP is amplifier + positive feedback. But the gain and phase shift provided by the feedback network depends on the frequency of the signal. 

At some frequency, the loop gain becomes unity and phase shift around the loop becomes 360 deg and the circuits starts oscillating (see Barkhausen Criteria). 

Conclusion: The input comes from noise. DC supply is for biasing the amplifier. The value of L and C decides the feedback factor and hence the frequency of operation.