TEOREMA TITIK TETAP AVERY-PETERSON DAN APLIKASINYA PADA MASALAH SYARAT BATAS p-LAPLACIAN BERDIMENSI SATU DENGAN DEVIASI ARGUMENT; AVERY-PETERSON FIXED POINT THEOREM AND APPLICATION OF ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY VALUE PROBLEMS WITH DEVIATING ARGUMENTS

MELIANA PASARIBU, Rini Indrati

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

In this final project we discuss about Avery-Peterson fixed point theorem and application. First we discuss Avery-Peterson fixed point theorem. This theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach Space. We continue by discussing about sufficient conditions that imply the existence and uniqueness of positive solutions of four-point boundary value problems for fourth-order ordinary differential equations with p-Laplacian. By using Avery-Peterson fixed point theorem, we formulate sufficient conditions so that boundary value problems have at least three positive solutions. Especially, we discuss such problems in the cases when the deviating arguments are advanced arguments

Kata Kunci : Fixed point theorem, Positive solutions, Fourth order differential equations, Advanced arguments, Delayed arguments