Theory And Methods Of Nonlinear Functional Analysis And Applications In Quantative Problems Of Equations

In this paper, they want to discuss the theory and the methods of nonlinear functional analysis and applications in qualified problems of equations. Three problems are studied in this paper.Firstly, they discuss the question on the nontrivial solutions of an initial value problem of a class of nonlinear ordinary differential equations in engineering ,proving the boundness and multiplicity of the nontrivial solutions .By using iteration , they want to prove the solvability of the problem .The paper ,which is published in Journal of Ocean University of China , is a complement to the results of a previouspaper ( W.Ora sin ski, On nontrivial solutions to some nonlinear ordinarydifferential equations)Secondly, they study the existence of multiple of nontrivial solutions of Hammerstein nonlinear integral equation , which is reduced to a system of integral equations .By using the methods of fixed point index in cones , some new existence theorems are obtained, which can be applied to the boundary value problems in ordinary differential equations .Thirdly, they discuss the existence and multiplicity of positive solutions of a class of second order m-point boundary value problem by using fixed point theorem in cones .