The Existence And Multiplicity Of Symmetric Positive Solutions For Nonlinear Boundary Value Problems

In this paper, we are concerned with the existence of symmetric positive so-lutions of the following fourth-order nonlinear boundary value problem with p-Laplacian operator and Stieltijes integral boundary conditions where λ>0,p>1,φp:Râ†'R is the p-Laplacian operator, i.e., φp(s)=|s|p-2s and (φp)-1=φq with1/p+1/q=1.Firstly, by using the Schauder fixed-point theorem, we obtain the sufficient condition which guarantee the existence of one symmetric positive solution for the nonlinear integral boundary value problem.Then, by employing the fixed-point theorem of functional type in a cones and some analytical skills, we study the multiplicity of symmetric positive solution non-linear integral boundary value problem and establish the sufficient condition which guarantee the existence of one symmetric positive solution for the integral boundary value problem.Finally, some examples are given to illustrate our main results.