On sequences of large homoclinic solutions for a difference equations on the integers involving oscillatory nonlinearities

2016/03/23 by Stegliński, Robert
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.07104

Abstract

In this paper, we determine a concrete interval of positive parameters λ, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem -Δ( a(k)ϕ_p(Δu(k-1))) +b(k)ϕ_p(u(k))=λf(k,u(k)), k∈ Z; where the nonlinear term f : Z × R → R has an appropriate oscillatory behavior at infinity, without any symmetry assumptions. The approach is based on critical point theory.

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