Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem

Research Article Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem

Two-point right focal eigenvalue problems on time scales

We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems (−1) n−p y Δ n (t) = λ f (t, y(σ n−1 (t)), y Δ (σ n−2 (t)),..., y Δ p−1 (σ n−p (t))), t ∈ [0,1] ∩ T, y Δ i (0) = 0, 0 ≤ i ≤ p − 1, y Δ i (σ(1)) = 0, p ≤ i ≤ n − 1, where λ > 0, n ≥ 2,1 ≤ p ≤ n − 1 are fixed and T is a time scale.

Positive Solutions for Semipositone Fourth-order Two-point Boundary Value Problems

In this paper we investigate the existence of positive solutions of the following nonlinear semipositone fourth-order two-point boundary-value problem with second derivative: u(t) = f(t, u(t), u′′(t)), 0 ≤ t ≤ 1, u′(1) = u′′(1) = u′′′(1) = 0, ku(0) = u′′′(0), where −6 < k < 0, f ≥ −M , and M is a positive constant. Our approach relies on the Krasnosel’skii fixed point theorem.

Positive Solutions of Two-point right focal boundary value problems on time scales

Multiple positive solutions to third-order three-point singular semipositone boundary value problem

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: x ′′′ (t) − λ f (t, x) = 0, t ∈ (0, 1); x(0) = x ′ (η) = x ′′ (1) = 0, where 1 2 < η < 1, the non-linear term f (t, x): (0, 1) × (0, +∞) → (−∞, +∞) is continuous and may be singular at t = 0, t = 1...