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In this thesis we study the problem of existence and multiplicity of positive periodic solution to the scalar ODE , , where is a positive function on , super linear at zero and sub linear at infinity, and is a -periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solution for some classes of nonlinearities when is small. Then, using critical point theory, we prove the existence of at least two positive -periodic solutions for large. Then, we prove the existence of a pair of positive -periodic solutions as well as the existence of positive sub harmonic solutions of any order for the scalar second order ODE where is same as above,... 

Ilam refinery has three synchronous generator units each with a capacity of 26.5 MVA and two six-phase LCI-fed synchronous compressors, each with a capacity of 8 MW. Generators of Ilam gas refinery have instability issue in case of island operation. With launching one generator unit and then connecting two compressors the instability problem and tripping of the generators appear. Given the importance of this issue, various tests and corresponding measurements in both electrical and mechanical aspects were carried out at the plant in on-grid and island operations to analyze the cause of instability phenomena. The mechanical part of tests analyses the frequency of oscillations and vibration in...