Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian

Abstract

a b s t r a c tIn this paper, we study the existence of positive solutions of the following nth-order fourpoint boundary value problem with one dimensional p-LaplacianBy using a fixed point theorem in cones, the existence of a positive solution and multiple positive solutions is obtained. Also, at the end of this paper, we present a generalization of this problem.

Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives

“…Owing to its significance in physics, the existence of positive solutions for the fourth-order boundary value problem has been studied by many authors using nonlinear alternatives of Leray-Schauder, the fixed point index theory, the Krasnosel'skii's fixed point theorem and the method of upper and lower solutions, in reference [1][2][3][4][5][6][7][8][9][10].…”

“…By the Krasnosel'skii's fixed point theorem in cone [11], Bai [5] investigated the following fourthorder boundary value problem with one parameter ⎧ ⎨ ⎩ u (4) (t) + βu (t) = λf (t, u(t), u (t)), 0 < t < 1, By the fixed point index in cone, Ma [7] proved the existence of symmetric positive solutions for the nonlocal fourth-order boundary value problem ⎧ ⎨ ⎩ u (4) (t) = h(t)f (t, u(t)), 0 < t < 1,…”