In this paper, we establish the solvability for integral boundary value problems of fractional differential equation with the nonlinear term dependent in a fractional derivative of lower order on infinite intervals. The existence and uniqueness of solutions for the boundary value problem are proved by means of the Schauder's fixed point theorem and Banach's contraction mapping principle. Finally, we give two examples to demonstrate the use of the main results.

A novel dynamic vibration absorber(DVA) model with negative stiffness and inerter-mass is presented and analytically studied in this paper. The research shows there are still two fixed points independent of the absorber damping in the amplitude frequency curve of the primary system when the system contains negative stiffness and inerter-mass. The optimum frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal negative stiffness ratio. Accordingly, the best working range of inerter is determined and optimal negative stiffness ratio and approximate optimal damping ratio are also obtained. At last the control performance of the presented DVA is compared with three existing typical DVAs. The comparison results in harmonic and random excitation show that the presented DVA could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation.

In this paper, we study the nonlinear second-order impulsive q k -difference equations with Sturm-Liouville type, in which nonlinear team and impulsive teams are dependent on first-order q k -derivatives. We obtain the existence and uniqueness results of solutions for the problem by Banach's contraction mapping principle and Schaefer's fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. c 2016 All rights reserved.Keywords: q k -derivative, q k -integral, impulsive q k -difference equation, boundary value problem, fixed point theorem. 2010 MSC: 39A13, 34B15, 34B37, 81Q99.

No abstract

In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations with p-Laplacian operator, in which q(t) can be singular at t = 0, 1. We also show that the results obtained can be applied to study certain higher order mixed boundary value problems. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.