I am getting false positive results after 35 cycles, when my positive samples come at around the 20th cycle. How can I optimize these kinds of problems?
The concentration in your samples is more than 30000 times higher that the "apparent" concentration of the negative controls. As long as you don't want to demonstrate the complete absence of the target sequence in your samples this is all perfectly ok.
If you want to demonstrate the complete absence of the target sequence in your samples, the false positive results may be disturbing. In this case you can use sequence-specific probes, or an elevated temperature at the measurement time (with SYBR Green), to get a specific signal. However, this does not solve the problem because the competeing amplification of the unspecific products (they are amplified, even if you do not detect them!) may hinder the efficient amplification of target molecules that are also present in the sample. The only real solution is to change the primers and possibly also the PCR buffer until the amplification is 100% specific.
Simply add one additional fluorescence reading step of 5s at 3ºC over the melting temperature of your PCR product in negative samples. It will minimize the fluorescence of primer dimer.