Splitting lemma at infinity and a strongly resonant problem with periodic nonlinearity

• DOI: 10.1007/s00526-006-0025-1
• Publication Date: 2006-04-12T13:12:34Z
• Authors: Shaowei Chen; Shujie Li
• Keywords: Infinity; Lemma (botany)

In this paper we study the following problem: $$-\triangle u-\lambda_{2}u=g(u)+h(x),\ x \in B,\ u(x)=0,\ x \in \partial B $$ with periodic nonlinearity g, where $$B=\{x\in \mathbb{R}^{2}\ |\ |x|<1\}$$ and λ2 is the second eigenvalue of −Δ, on H 1 0(B). We proved that the problem has infinitely many solutions under some additional conditions on g and h. The method we used is a new variational reduction method.