Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations
نویسندگان
چکیده
where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equation
منابع مشابه
Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملEXISTENCE OF PERIODIC SOLUTIONS FOR 2nTH-ORDER NONLINEAR p-LAPLACIAN DIFFERENCE EQUATIONS
By using the critical point theory, the existence of periodic solutions for 2nth-order nonlinear pLaplacian difference equations 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 2nth-order p-Laplacian difference equations. The results obtained successfully generalize and co...
متن کاملEXISTENCE OF PERIODIC SOLUTIONS OF 2α-ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p−LAPLACIAN
The existence of periodic solutions of a higher order nonlinear functional difference equation with p-Laplacian is studied. Sufficient conditions for the existence of periodic solutions of such equation are established. The result is based on Mawhin′s continuation theorem. The methods used to estimate the priori bound on periodic solutions are very technical.
متن کاملExistence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
متن کاملTriple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian
In this paper, we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly. Our results ...
متن کامل