POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

Positive Solutions to a Singular Second Order Boundary Value Problem

In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...

Positive Solutions to a Second-Order Discrete Boundary Value Problem

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

Existence of Positive Solutions of a Nonlinear Second-order Boundary-value Problem with Integral Boundary Conditions

In this article we prove the existence of at least one positive solution for a three-point integral boundary-value problem for a second-order nonlinear differential equation. The existence result is obtained by using Schauder’s fixed point theorem. Therefore, we do not need local assumptions such as superlinearity or sublinearity of the involved nonlinear functions.

Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter

This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is pr...