Positive solution for fourth-order m-point nonhomogeneous boundary value problems

Abstract

This paper is concerned with the following fourth-order m-point nonhomogeneous boundary value problemwhere a i ≥ 0 (i = 1, 2, . . . , m − 2), 0 < ξ 1 < ξ 2 < · · · < ξ m−2 < 1 and m−2 i=1 a i ξ i < 1, and λ > 0 is a parameter. The existence and nonexistence of positive solution are discussed for suitable λ > 0 when f is superlinear or sublinear. The main tool used is the well-known Guo-Krasnoselskii fixed point theorem.

Solvability of Third-Order Three-Point Boundary Value Problems

“…Substituting (13) and (14) into (12), the problem (1)-(2) is equivalent to the following integral equation:…”

“…Recently, the existence of solutions for boundary value problem has been investigated by many authors [1][2][3][4][5][6][7][8][9]. Further, many authors focused on the existence of solutions or positive solutions for higher order differential equations with boundary value problems [10][11][12][13][14][15][16].…”