Existence Of Positive Solutions For Fourth-order Nonlinear Integral Boundary Value Problems

In this paper, we mainly study the problem on the existence of one and multiplepositive solutions of integral boundary value problems for a class of fourth-ordernonlinear differential equations. First, we study the problem on the existence of oneand multiple positive solutions for the following fourth-order integral boundary valueproblemsBy employing the cone compression and extension fixed point theorem and someanalytical skills, we establish some sufficient conditions which guarantee theexistence of one and multiple positive solutions for the integral boundary valueproblems. Our results generalize and improve the relative results of the paper [1]. Next,we study the problem on the existence of one and multiple positive solutions of theboundary value problem for the following fourth-order singular nonlinear differentialequations with sign-changing nonlinear term and nonlinear integral boundaryconditionsWe establish some new results on the existence of one and multiple positive solutionsfor the boundary value problems. Our results extend and improve the relative results ofthe paper [16], for example, further to expand the boundary value conditions of theboundary value problem and relax the sign-changing condition on the right functionf and so on.In addition, some examples are given to illustrate our main results in Chapter2andChapte3, respectively.