Multiple positive solutions for one-dimensional p-Laplacian boundary value problems

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.

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

EXISTENCE OF POSITIVE PSEUDO-SYMMETRIC SOLUTIONS FOR ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY-VALUE PROBLEMS

We prove the existence of positive pseudo-symmetric solutions for four-point boundary-value problems with p-Laplacian. Also we present an monotone iterative scheme for approximating the solution. The interesting point here is that the nonlinear term f involves the first-order derivative.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...

MULTIPLE POSITIVE SOLUTIONS FOR FOURTH-ORDER THREE-POINT p-LAPLACIAN BOUNDARY-VALUE PROBLEMS

In this paper, we study the three-point boundary-value problem for a fourth-order one-dimensional p-Laplacian differential equation ` φp(u ′′(t)) ́′′ + a(t)f ` u(t) ́ = 0, t ∈ (0, 1), subject to the nonlinear boundary conditions: u(0) = ξu(1), u′(1) = ηu′(0), (φp(u ′′(0))′ = α1(φp(u ′′(δ))′, u′′(1) = p−1 p β1u ′′(δ), where φp(s) = |s|p−2s, p > 1. Using the five functional fixed point theorem due...