We present some fixed point results for mappings which satisfy Hardy-Rogers rational type, quasicontraction type, weak contraction type and generalized fΨ type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possible applications of our results to well-posed and limit shadowing property of fixed point problems is also presented.