Positive Solutions For Several Classes Of Boundary Value Problems Of Third-Order Differential Equations

Third-order diferential equations arise in a variety of diferent areas of appliedmathematics and physics, for example, in the defection of a curved beam havinga constant or varying cross section, a three-layer beam, electromagnetic waves orgravity driven fows and so on. Recently, boundary value problems (BVPs for short)of third-order diferential equations have attracted a lot of attention for its wideapplication background and practical background. Therefore, it is signifcant tostudy the BVPs of third-order diferential equations.The paper is divided into four chapters:In Chapter1, the research background and the main work of the paper isoutlined, and some preliminary knowledge is given.In Chapter2, aiming at a class of nonlinear third-order three-point BVP, thecorresponding Green’s function is given and its properties are discussed. And then,the existence of positive solution is obtained by using the Guo-Krasnoselskii fxedpoint theorem.In Chapter3, a class of third-order BVP with integral boundary conditions isconsidered. The existence of monotone positive solution is obtained when the non-linear term is superlinear or sublinear. The main tool used is the Guo-Krasnoselskiifxed point theorem.In Chapter4, a class of third-order BVP with integral boundary conditions isdiscussed using monotone iterative method. From the above, the existence of mono-tone positive solution is obtained and one iterative sequence of monotone positivesolution is given. It is worth mentioning that the iterative scheme starts of withzero function, which is useful and feasible for computational purpose. Finally, wegive an example to illustrate the main results.