Existence and iteration of monotone positive solutions for an elastic beam equation with a corner

A sum operator equation and applications to nonlinear elastic beam equations and Lane–Emden–Fowler equations

“…The boundary condition u (1) = 0, u (1) = g(u(1)) means that the right end of the beam is attached to a bearing device, given by the function g. Fourth-order two-point boundary value problems are useful for mechanics of materials because the problems usually characterize the deformations of an elastic beam. The existence and multiplicity of positive solutions for the elastic beam equations have been studied extensively, see for example [3,7,18,28,29,35,37,40] and references therein. But in the existing literature, there are few papers concerned with the uniqueness of positive solutions.…”

“…Because of the crucial role played by nonlinear equations in the applied science as well as in mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators which arise in the connection with nonlinear differential and integral equations have been extensively studied over the past several decades (see, for instance, [2,3,5,23,[35][36][37]40]). The existence and uniqueness of positive solutions to nonlinear operator equations is very important in theory and applications.…”

Monotone iteration method for differential equations involving integral boundary conditions on the half line

“…Recently an increasing interest has been observed in investigating the existence of positive solutions of boundary value problems for differential equations by using the monotone iterative method [1][2][3][4][5][6][7][8][9][10][11][12].…”

Existence of positive solutions to a non-positive elastic beam equation with both ends fixed

“…The problem (P) describes the deflection of an elastic beam with both ends rigidly fixed. The existence and multiplicity of positive solutions for the elastic beam equations has been studied extensively when the non-linear term f : [0,1] × [0, +∞) [0, +∞) is continuous, see for example [1][2][3][4][5][6][7][8][9][10] and references therein. Agarwal and Chow [1] investigated problem (P) by using of contraction mapping and iterative methods.…”