Positive Solutions for a Second-Order p

The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u,  00 and μ>0 are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of λ>0 and μ>0. The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by Ding and Wang

Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional <inline-formula> <graphic file="1687-2770-2011-654871-i1.gif"/></inline-formula>-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 -Laplacian. Moreover, we offer some interesting discussion of the associated boundary value problems. Upper and lower bounds for these positive solutions also are given, so our work is new.</p

Periodic Solutions and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

The Rayleigh equation with two deviating arguments x′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t) is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results

A class of singular kik_i-Hessian systems

Our main objective of this article is to investigate a class of singular $k_i$-Hessian systems. Among others, we obtain new theorems on the existence and multiplicity of positive radial solutions. Several nonexistence theorems are also derived