Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result

Existence and Uniqueness of Positive Solutions for a Fractional Switched System

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant function depending on t, and ℝ+=[0,+∞),  fi,gi∈C[J×ℝ+,ℝ+], i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results

Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator

We discuss the existence of solutions about generalized antiperiodic boundary value problems for the fractional differential equation with p-Laplacian operator , , , , , , where is the Caputo fractional derivative, , , , and , , , . Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results