The Method of Lower and Upper Solutions for a Bending of an Elastic Beam Equation

Positive Solutions of Some Fourth-order Two Point Boundary Value Problem 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] [11]. In recent years, there has been much attention on the fourth-order differential equations with one or two parameters.…”

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].…”

The existence of multiple positive solutions for a class of semipositone Dirichlet boundary value problems

“…Nonlinear boundary value problems, as an important branch of modern applied mathematics, have been studied by many authors in recent years [1,4,[7][8][9][10][11]. In the study The second author is financially supported by the National Natural Science Foundation of China (11071141, 10771117) and the Natural Science Foundation of Shandong Province of China (Y2007A23, ZR2010AM017).…”