Three positive solutions for the one-dimensional p-Laplacian

Positive solutions for a multi - point eigenvalue problem involving the one dimensional p - Laplacian ∗ †

A multi-point boundary value problem involving the one dimensional p-Laplacian and depending on a parameter is studied in this paper and existence of positive solutions is established by means of a fixed point theorem for operators defined on Banach spaces with cones.

The Existence of Three Positive Solutions to Integral Type BVPs for Second ODEs with One-dimensional p-Laplacian

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian  [ρ(t)Φ(x′(t))]′ + f(t, x(t), x′(t)) = 0, t ∈ (0, 1), φ1(x(0)) = ∫ 1 0 g(s)φ1(x(s))ds, φ2(x ′(1)) = ∫ 1 0 h(s)φ2(x ′(s))ds. Sufficient conditions to guarantee the existence of at least three positive solutions of this BVP are established. An exampl...

Three Solutions for a Mixed Boundary Value Problem Involving the One-dimensional P-laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [To...

Rectifiability of Solutions of the One-dimensional P-laplacian

In the recent papers [8] and [10] a class of Carathéodory functions f(t, η, ξ) rapidly sign-changing near the boundary point t = a, has been constructed so that the equation −(|y′|p−2y′)′ = f(t, y, y′) in (a, b) admits continuous bounded solutions y whose graphs G(y) do not possess a finite length. In this paper, the same class of functions f(t, η, ξ) will be given, but with slightly different ...

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