The phrase "there exist difficulties" is grammatically correct and can be used in written English.
It is often used to indicate that there are challenges or obstacles present in a situation. Example: "Despite their determination, there exist difficulties in implementing the new company policy." This sentence means that even though the employees are determined to make the new policy work, they are facing challenges in doing so.
There exists difficulty in monitoring the efficacy of bolus transport through the deglutitive apparatus in vivo, especially in patients which exhibit pathological difficulties.
Finding a high accurate and efficient numerical method has become a significant research due to except for a few number of these equations, there exists difficulty to find the exact solution of fractional differential equations (FDEs).
There also exist difficulties in transmitting braking signal and pressure between the assisting and disabled train.
It should be pointed out that there exist a number of difficulties encountered in the study of the stability for mild solution to neutral stochastic partial differential equations with delays since the neutral item is present.
In Algorithms 3.1 and 3.2, there still exists difficulty to implement the projections P C and P Q with respect to the defined norms, especially when C and Q are general closed convex sets.
However there exist some difficulties.
Different from one-dimensional Hamiltonian systems, there exist two difficulties in higher-dimensional beam equations.
However, there exist some difficulties and complexities to address the structure of the Green function for these boundary value problems.
The hybrid flow shop scheduling with multiprocessor task (HFSMT) problem is a substantial production scheduling problem for minimizing the makespan, and there exist many difficulties in solving large scale HFSMT problems which include many jobs, machines and tasks.
In addition, there exist some difficulties such as the failure of the monotonicity of the energy functional, the anisotropy of the diffusive operator and the gap between the norm and the modular, which make the methods used in [19] fail.
