We prove the existence of homoclinic solutions for second order Lagrangian systems of the type —ue + u = α(t)▽G(u) in R~N where G ∈ C~2(R~N, R) is superquadratic and α ∈ C~1(R, R) satisfies the condition lim_(∣t∣→ ∞) α(t) = 0. The method is variational: solutions being found as critical points of a suitable action functional. We prove the existence of at least one nontrivial critical point using the analysis of problems "at infinity" and level comparison arguments.
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机译：我们证明了R〜N中类型为-ue + u =α（t）▽G（u）的二阶拉格朗日系统的同宿解的存在，其中G∈C〜2（R〜N，R）是超二次的，而α ∈C〜1（R，R）满足lim_（∣t∣→∞）α（t）= 0的条件。该方法是可变的：找到适合的作用函数的临界点的解。通过对“无穷大”问题和层次比较论点的分析，我们证明了至少一个重要的临界点的存在。
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