Singular Discrete Boundary Value Problems Research Articles

Existence to singular discrete boundary value problems with sign changing nonlinearities using approximation methods

In this paper we use approximation methods to examine the singular discrete boundary value problem \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\{ \begin{gathered} - \Delta ^2 u(k - 1) = g(k,u(k)) + h(k,u(k)),k \in [1,T] \hfill \\ u(0) = 0 = u(T + 1) \hfill \\ \end{gathered} \right.$$ \end{document} where our nonlinearity may be singular in its dependent variable and is allowed to change sign.

Singular discrete second order BVPs with p-Laplacian

We study singular discrete boundary value problems with mixed boundary conditions and with the p-Laplacian of the form where , , , p>1. We assume that f is continuous on and has a singularity at x=0. We prove the existence of a positive solution by means of lower and upper functions method, Brouwer fixed point theorem and by a convergence of approximate regular problems.

A positive solution for singular discrete boundary value problems with sign-changing nonlinearities

This paper presents new existence results for the singular discrete boundary value problem −Δ2u(k−1)=g(k,u(k))+λh(k,u(k)), k∈[1,T], u(0)=0=u(T+1). In particular, our nonlinearity may be singular in its dependent variable and is allowed to change sign.

A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems for the One-Dimensional p-Laplacian

This paper presents new existence results for singular discrete boundary value problems for the one-dimension p -Laplacian. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. Our results are new even for p = 2.

Multiple positive solutions of singular and nonsingular discrete problems via variational methods

We employ the critical point theory to establish the existence of multiple solutions of some regular as well as singular discrete boundary value problems.

Positive solutions for singular discrete boundary value problems

We study the existence of zero‐convergent solutions for the second‐order nonlinear difference equation Δ(anΦp(Δxn)) = g(n, xn+1), where Φp(u) = |u|p−2u, p > 1,{an} is a positive real sequence for n ≥ 1, and g is a positive continuous function on ℕ × (0, u0), 0 < u0 ≤ ∞. The effects of singular nonlinearities and of the forcing term are treated as well.

Singular discrete boundary value problems

This paper discusses the discrete problem Δ 2 y( i − 1) + f( i, y( i)) = 0, i ∈ {0,…, T}, y(0) = y( T + 1) = 0 where our nonlinear term f( i, u) may be singular at u = 0.