... local minimum of Φ in H with c1:Φv20 >c0.At this point, we can apply Lemma 2.5 taking Ψ and −Ψ as perturbing terms. Then, for ∈ 0,rδ small enough and any ρ1∈ c0, min {b, ... c1}, ρ2∈ 0, ∞, we can obtain thefollowing.4 Boundary Value ProblemsFinding solutions of problem 1.1 is equivalent to finding critical points of I :ΦλΨ in H andIu,vω0eσsusvsds ... have been in electronics, butit can also have applications in mechanics and in biology. For example, the brain is full ofoscillators at micro and macro levels 2. There are applications in neurology,...