Xuemei Zhang

Positive Solutions of th-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions

This paper is devoted to study the existence, nonexistence, and multiplicity of positive solutions for the th-order nonlocal boundary value problem with impulse effects. The arguments are based upon fixed point theorems in a cone. An example is worked out to demonstrate the main results.

Positive solutions for classes of multi-parameter fourth-order impulsive differential equations with one-dimensional singular p-Laplacian

The authors consider the following impulsive differential equations involving the one-dimensional singular p-Laplacian: (ϕp(y″(t)))″=λω(t)f(t,y(t)), t∈J, t≠tk, k=1,2,…,m, Δy′|t=tk=−μIk(tk,y(tk)), k=1,2,…,m, ay(0)−by′(0)=∫01h(s)y(s)ds, ay(1)+by′(1)=∫01h(s)y(s)ds, ϕp(y″(0))=ϕp(y″(1))=∫01h(t)ϕp(y″(t))dt, where λ>0 and μ>0 are two parameters. Several new and more general existence and multiplicity results are derived in terms of different values of λ>0 and μ>0. In this case, our results cover equations without impulsive effects and are compared with some recent results.

Positive Solutions of Open image in new window th-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions

This paper is devoted to study the existence, nonexistence, and multiplicity of positive solutions for the th-order nonlocal boundary value problem with impulse effects. The arguments are based upon fixed point theorems in a cone. An example is worked out to demonstrate the main results.