Existence and multiplicity of solutions for a class of Hamiltonian systems - Khachnaoui, Khaled (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.9 We investigate a class of Hamiltonian systems gather* -q’’(t)+(L(t)-ξ)q(t)= a(t)|q(t)|^p-2q(t)+η f(t), qH^1(R,R^N),gather* where (t,q)R× R^N, p>2, aC(R,(0,+∞)), fC(R,R^N), ξ, η are real parameters, and LC(R,R^N^2) is a positive definite symmetric matrix for all tR. The main technical approach is based on the Nehari manifold method combined with variational and topological methods. The obtained results extend and complement the results available in the literature.