Multiple Positive Solutions for Second-Order p-Laplacian Dynamic Equations with Integral Boundary Conditions

Multiple Positive Solutions for Second-Order p-Laplacian Dynamic Equations with Integral Boundary Conditions

Copyright q 2011 Y. Li and T. Zhang. 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 properly cited. We are concerned with the following second-order p-Laplacian dynamic equations on time scales ϕ p x Δ t ∇ λft, xt, x Δ t 0, t ∈ 0, T T , with int...

Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C3 0, 1 as well as C2 0, 1 positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t 0, t 1, and u 0. The dual results for the other integral b...

Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian

By using the fixed point theory for completely continuous operator, this paper investigates the existence of positive solutions for a class of fourth-order impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian. Moreover, we offer some interesting discussion of the associated boundary value problems. Upper and lower bounds for these positive solution...

Positive Solutions for p-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

where α and β are nonnegative constants. Boundary value problems of ordinary differential equations arise in kinds of different areas of applied mathematics and physics. Many authors have studied two-point, threepoint, multi-point boundary value problems for second-order differential equations extensively, see [–] and the references therein. In recent years, boundary value problems with integ...