[PDF] Top 20 A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type

... Newtonian type forces or to restor- ing forces caused by compressed ...the existence of a positive periodic solution is that e ¯ := T   T e(s) ds < ...the existence of periodic ... See full document

... differential equations was paid to investigating the problem of periodic solutions for second order differential equations with ...the singularity has a significant background in applied ... See full document

... the existence of positive periodic solutions for equation ...lower solutions methods used in [20, 21], and continuation theorems of coincidence degree used in ...the periodic problem ... See full document

... lower solutions, was first used by Lazer and Solimini in the pioneering paper [] for considering the problem of a periodic solution to a second order differential equations with ... See full document

... the existence of positive periodic solutions to ...(weak singularity condition), some equations like ...the equations have no T -periodic ...the periodic problem ... See full document

... the equations with a singular- ity began with some work of Forbat and Huaux ...the equations studied previously were either of the type of Duffing equations [–, –] or of the type ... See full document

... This paper is concerned with the existence of positive periodic solutions for the prescribed mean curvature Rayleigh equations with a singularity. Our results are based on the ... See full document

... the existence of pe- riodic solutions by using topological degree ...the existence of positive periodic solutions of ...consider repulsive type and attractive ...main ... See full document

... the Rayleigh equations. More recently, the existence of periodic solutions for Rayleigh equa- tion was extensively studied (see [2–11] and the references ...study Rayleigh ... See full document

... Nowadays, the prescribed mean 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 ... See full document

... the existence of positive periodic solutions for some types of differential equations with a singularity have been obtained; see [–] and the references cited ...the periodic ... See full document

... The structure of the paper is as follows. Section  contains the tools needed in the proofs. In Section , we state and prove the main results and develop some corollaries for the equation with a singularity of ... See full document

... to equations with repulsive singularity or equations with time-independent deviating ...a new question arises: how the Rayleigh equation with attractive singularity works ... See full document

... the existence of Aubry-Mather sets and quasi- periodic solutions of equation ...a new estimate approach and apply a kind of analytical techniques developed by the present author (see the ... See full document

... concerning periodic solutions of partial differential equations has become an important area of investigation in recent ...the periodic problems of abstract evolution equations in the ... See full document

... P ro o f (i) Let x be a 4-periodic solution o f (1). Then x can be presented by (9), where (x (0 ),x (-2 ),x '(-2 )) is the solution o f (11). The linear system (11) is solvable if and only if D 2(p,q) = 0. Hence ... See full document

... it follows that problem (.) admits a solution. It is easily seen that the result of [] cannot be applied to this case. Note that one can also obtain the solvability of (.) in this case by the result ... See full document

... a periodic time scale which has the subspace topology inherited from the standard topology on ...the existence of periodic solutions for such equations, which generalize many known ... See full document

... This fractional integral has also been extended to fractional derivative in [6], which holds “nicely” for α with Re(α) ∈ (0, 1) (see [6, § 3]). Motivated by the definition of fractional order derivatives given in [6], we ... See full document

... From the analysis of Eq. (12) it is evident that on its left-hand side there is only an angular accel- eration coming from the bending moment, and on its right-hand side there is a sum of all the moments of the forces ... See full document