The Existence Of Solutions For One Class Of System Of Fractional Nonlinear Schr(o|¨)dinger Equations

Fractional partial diferential equations are one of the important equations in optics, electro-magnetism, quantum mechanics, fluid mechanics, atomic physics, quantum mechanical systems,etc. They have been studied broadly and deeply by many scholars which means that lots of prob-lems about fractal dimension can be solved easily. The fractional partial diferential equations havesignificant background. They can describe essential nature problems more accurately. Fractionalpartial diferential equations possess prominent study values and wide prospects of research. Theresearch of related properties and applications about fractional partial diferential equations be-comes the hot spots for the present work. They have been gotten breakthrough on the numericalsolution, the accurate solution and the well-posedness of the solution.In this paper, we discussed the existence of solution and presence of global attractor for severalkinds of fractional nonlinear Schr(o|¨)dinger equations. We researched the existence and uniquenessof the solutions for a class of generalized fractional nonlinear Schr(o|¨)dinger equations, the globalsolutions of the periodic boundary value problem for a class of fractional nonlinear Schro¨dingerequation with multiple potential, the existence and uniqueness of the global smooth solutions forone class of weakly damped driven fractional nonlinear Schr(o|¨)dinger Equation.chapter1, we introduced the physical background of the fractional partial diferential equationsand the main results in our paper. We also gave some definitions and theorems of our thesis.chapter2, we investigate the existence and uniqueness of solutions for a class of generalizedfractional nonlinear Schr(o|¨)dinger equations. Firstly, made a priori estimates to the solution, usingGagliardo-Nirenberg inequality, Young inequality and Gronwall inequality. Secondly, get the ex-istence of solution by Faedo-Gal¨erkin method. Finally, we proofed the uniqueness of solutions forequations.chapter3, we proved the periodic boundary value problem of the global smooth solution forfractional nonlinear Schr(o|¨)dinger equation with multiple potential.chapter4, we introduced the existence and uniqueness of the global smooth solutions for oneclass of weakly damped driven fractional nonlinear Schr(o|¨)dinger Equation.chapter5, we get a summary of this thesis and points out the further plan of work.