Abstract In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized boundary conditions satisfying the monotone assumptions. Our new results unify existence criteria of linear and value problems (BVPs) that have been previously studied on case-by-case basis; for example, Dirichlet Neumann are special cases. The common feature is solution each B...

The concept of concavity is generalized to functions, y, satisfying nth order differential inequalities, (−1)n−ky(n)(t) ≥ 0, 0 ≤ t ≤ 1, and homogeneous two-point boundary conditions, y(0) = . . . = y(k−1)(0) = 0, y(1) = . . . = y(n−k−1)(1) = 0, for some k ∈ {1, . . . , n− 1}. A piecewise polynomial, which bounds the function, y, below, is constructed, and then is employed to obtain that y(t) ≥ ...

This paper is concerned with the existence of multiple positive solutions for the third-order pLaplacian dynamic equation φp uΔ∇ t ∇ a t f t, u t , uΔ t 0, t ∈ 0, T T with the multipoint boundary conditions uΔ 0 uΔ∇ 0 0, u T B0 ∑m−2 i 1 biu Δ ξi 0, where φp u |u|p−2u with p > 1. Using the fixed point theorem due to Avery and Peterson, we establish the existence criteria of at least three positi...

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This is based on basis functions with for the second-order derivative. The theoretical derivative and error analysis have been successfully derived. We found that was O(h3) accurate. By using approximation, proposed O(h5) Four numerical consisting of ordinary dif...

This paper is concerned with the numerical solution of a system of ordinary di erential equations ODEs y Sy t f t y p on an inter val b subject to boundary conditions g y y b p The ODEs have a coe cient that is singular at t but it is assumed that the boundary value problem BVP has a smooth solution Some popular methods for BVPs evaluate the ODEs at t This paper deals with the practical issues ...