Solvability Of Boundary Value Problems For Several Classes Of Higher-order Differential Equations

In this paper, we discuss solvability of boundary value problems for several class-es of higher-order differential equations with the tools of fixed point index principle, Guo-Kra.snoselskii fixed point theorem and Leray-Schauder theorem. The specific content are listed as follows:In section one, by using fixed point index theory, we study the existence of positive solutions for the boundary value problemAnd by using Guo-Krasnoselskii fixed point theory, we discuss the range of parameter λ, when boundary value problem has positive solution, where η∈ (0.1), α, β≥ 0. A is parameter and λ> 0.In section two. we discuss solvability of the following higher-order differential equation boundary value problemIn section three, by using A very-Peterson fixed point theory, we consider the existence of three positive solutions for the following higher-order boundary value problem where n≥ 2, p ∈{1,2, …, n-2}.In section four, by using the Leggett-Williams fixed point theory, we prove the existence of three positive solutions for the following fourth-order boundary value problem where p> 1, ξ, η ∈ (0,1), α,α ∈ (0,1).