Mathematical Sciences: Non-autonomous Differential Equations

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The goal of this project is the development and application of topological and analytical methods useful for the study of existence, multiplicity, and stability of solutions of nonlinear nonautonomous differential equations. The fact that the equations are forced or have temporal dependence complicates them considerably. Differential equations with forcing model a wide variety of phenomena that occurs in everyday life. Problems with nonlinearities near resonance are very complicated and require very sophisticated mathematics to give qualitative information.