A note on singular nonlinear boundary value problems for the one-dimensional p-Laplacian

Positive solutions for one-dimensional p-Laplacian boundary value problems with nonlinear parameter

In this paper, we establish existence of positive solutions of the nonlinear problems of one dimensional p-Laplacian with nonlinear parameter φp(u ′(t))′ + a(t)f(λ, u) = 0, t ∈ (0, 1), u(0) = u(1) = 0. where a : Ω→ R is continuous and may change sign, λ > 0 is a parameter, f(λ, 0) > 0 for all λ > 0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.

Analysis and Numerical Approximation of a Singular Boundary Value Problem for the One-dimensional p-Laplacian

In this work we are concerned about a singular boundary value problem involving the p-laplacian which arises in mathematical models of fluid mechanics. We analyze the asymptotic behavior of the solutions of the considered ordinary differential equation near the singularities and introduce a computational method which takes this behavior into account. Key–Words: Singular boundary value problem, ...

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.

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian

Positive Solutions for Discrete Boundary Value Problems to One-Dimensional p-Laplacian with Delay