In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator { (−∆)su+ V (|x|)u+ φ(|x|, u) = f(|x|, u), x ∈ R3, (−∆)tφ = u2, x ∈ R3, (1) where (−∆)s(s ∈ (0, 1)) and (−∆)t(t ∈ (0, 1)) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions. c ©2016 All rights reserved.

The existence of time periodic solutions of nonlinear wave equations utt −∆nu + ` n− 1 2 ́2 u = g(u)− f(t, x) on n-dimensional spheres is considered. The corresponding functional of the equation is studied by the convexity in suitable subspaces, minimax arguments for almost symmetric functional, comparison principles and Morse theory. The existence of infinitely many time periodic solutions is o...

Aixia Qian1 and Chong Li2 1 School of Mathematic Sciences, Qufu Normal University, Qufu Shandong 273165, China 2 Institute of Mathematics, AMSS, Academia Sinica, Beijing 100080, China Correspondence should be addressed to Aixia Qian, [email protected] and Chong Li, [email protected] Received 29 August 2009; Accepted 7 November 2009 Academic Editor: Wenming Zou Copyright q 2010 A. Qian and C. L...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...