[PDF] Top 20 Singularities of attractive and repulsive type for p Laplacian generalized Liénard equation

... where the nonlinear term g has a singularity of repulsive type. The author showed that Eq. (1.3) has at least one periodic solution by applications of coincidence degree theory. Zhang’s work has attracted ... See full document

... Inspired by the above paper [7], in this paper, we further consider the existence of a positive T -periodic solution for equation (1.1) with strong singularities of attractive and repulsive ... See full document

... where the nonlinear term g has a strong singularity of repulsive type at u = 0 and satisfies super-linearity condition at u = + ∞ . It is concluded that there exist infinitely many pos- itive periodic ... See full document

... with singularities of repulsive type ...sive type, the attractive case did not attract much attention of mathematical ...with attractive singularities [7, 16, 17, ...the ... See full document

... mixed singularities is at this moment very incomplete, and few references can be cited (see [, –]) if compared with the large number of references devoted to singular equations either of attractive or ... See full document

... (.) was investigated for the conservative case, i.e., f (x) ≡ . But the function ϕ(t) is re- quired to be ϕ(t) ≥  for all t ∈ [, T ]. The method of topological degree theory, together with the technique of upper and ... See full document

... (repulsive restoring force), where α >  is a constant and h : R → R is a T-periodic contin- uous function. A necessary condition for the existence of a positive T -periodic solution of equation (.) is ... See full document

... an attractive singularity and ...differential equation with repulsive singularity and, based on Schaefer’s fixed point theorem, new conditions for the existence of periodic solutions were ...the ... See full document

... the type of Duffing equations [–, –] or of the type of Liénard equations [, , , ...following p-Laplacian Liénard equations with a ... See full document

... curvature equation and its modified forms, which arise from some problems associated with differential geometry and physics such as com- bustible gas dynamics, have been studied widely (see [–] and the references ... See full document

... Rayleigh equation or neutral Rayleigh equa- tion with singularity of repulsive ...how p-Laplacian neutral Rayleigh equation works on singularity of attractive type? ... See full document

... The paper is organized as follows: In Sect. 2, we first analyze qualitative properties of the neutral operator (Au)(t) in the case that |c| > 1, which will be helpful for further studies of differential equations with ... See full document

... theorem, we state and prove the existence of a positive periodic solution for (.) with at- tractive singularity. In Section , we investigate the existence result for (.) with repulsive singularity. In Section ... See full document

... In the past years, much attention from researchers in differential equations was paid to investigating the problem of periodic solutions for second order differential equations with singularities. This is due to the ... See full document

... derstand a function u : [, ω] → R which is positive, absolutely continuous together with its first derivative, satisfies (.) almost everywhere on [, ω], and verifies (.). In spite of the fact that the problem (.), ... See full document

... In the past years, researchers paid much attention to investigating the problem of periodic solutions for second-order equations with singularities (see [1–16]). Among those studies, the study of properties of ... See full document

... fuzzy-logic-based attractive/repulsive ...graph Laplacian is introduced to overcome the difficulties in theoretical ...fuzzy-logic-based attractive/repulsive function is proposed for ... See full document

... The paper is organized as follows. In Section , we recall some basic concepts on frac- tional calculus and establish some preliminary results that will be used in Section , where we state and prove our main result. In ... See full document

... Our discussion is based on some results on the ranges for maximal monotone operators and pseudo-monotone operators in [–]. Some new methods of constructing appro- priate mappings to achieve our goal are employed. ... See full document

... is attractive force and second one is repulsive ...generate repulsive force to the robot that is inversely proportional to the distance from the robot to obstacles and is pointing away from ... See full document