Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems

Abstract EN

We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition 0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, where μ,ν>1 and 1/μ+1/ν=1 and α(n),β(n), and γ(n) are real-valued functions defined on ℤ.