'there often exists' is a correct and usable phrase in written English.
You might use it to introduce an idea or truth that is true a lot of the time, but not always. For example: "There often exists a tension between modernity and tradition."
In any system of coupled resonators there often exists a so-called "strongly coupled" regime of operation.
In a free of charge or flat-rate Internet access environment, there often exists abusive and unfair usage of network resources.
In addition, there often exists multiple models to represent the given situation, and complete confidence in selecting the most accurate model among the model set considered is beyond the capability of the user.
In addition, there often exists an underlying sentiment that urban kids should not be wasting time on holistic programs and non-academic achievement when so much improvement is needed in basic reading and math skills.
In such environment, there often exists inter-carrier interference.
In the process of the formal institution's implementation, there often exists a "decoupling of expression and practice".
In data sets with a hierarchical structure, there often exist correlations between observations that may result in overestimated differences in profiling analyses.
A probabilistic framework offers the flexibility to account for prior information, which can be useful, as some genes are more likely to be mutated in particular cancers and there often exist mutational hotspots within a gene.
There often exist many secondary data that must be considered in geostatistical reservoir modeling.
However, there often exist various perturbations in many real physical processes [8, 9, 10].
More specifically, in such networks, there often exist a large number of uncoordinated battery-powered devices with power resources.
