ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS

On periodic solutions of 2-periodic Lyness' equations

We study the existence of periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5–periodic. We prove that for each pair (a, b) 6= (1, 1) there are infinitely many initial conditions giving ris...

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

On Periodic Solutions of Abstract Differential Equations

Periodic Solutions of Lagrange Equations

Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.