Existence of periodic solutions for p-Laplacian neutral Rayleigh equation

Existence of periodic solutions for p-Laplacian neutral Rayleigh equation

where φp(x) = |x|p–x for x =  and p > ; σ and c are given constants with |c| = ; φp() = , f () = . The conjugate exponent of p is denoted by q, i.e.  p +  q = . f , g , β , e, and τ are real continuous functions on R; τ , β , and e are periodic with periodic T , T >  is a constant; ∫ T  e(t)dt = , ∫ T  β(t) = . As we know, the p-Laplace Rayleigh equation with a deviating argumen...

On the Existence of Periodic Solutions to a P -laplacian Rayleigh Equation

Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type

In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, [Formula: see text] By applications of an extension of Mawhin's continuation theorem, sufficient conditions for the existence of periodic solution are established.

Positive periodic solution for higher-order p-Laplacian neutral singular Rayleigh equation with variable coefficient

where p > , φp(x) = |x|p–x for x =  and φp() = , c ∈ Cn(R,R) and c(t + T) ≡ c(t), f is a continuous function defined in R and periodic in t with f (t, ·) = f (t + T , ·) and f (t, ) = , g(t,x) = g(x) + g(t,x), where g : R × (, +∞) → R is an L-Carathéodory function, g(t, ·) = g(t + T , ·), g ∈ C((,∞);R) has a singularity at x = , e : R→ R is a continuous periodic function with ...

Existence of periodic solutions for a 2nth-order difference equation involving p-Laplacian∗

By using the critical point theory, the existence of periodic solutions for a 2nth-order nonlinear difference equation containing both advance and retardation involving p-Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2nth-order p-Laplacian difference equation...