Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent
Department of Mathematics, University of California,
Irvine, CA 92697-3875, USA; firstname.lastname@example.org.
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; email@example.com.
In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation , where N ≥ 4; V,K,g are periodic in xj for 1 ≤ j ≤ N and 0 is in a gap of the spectrum of -Δ + V; K>0. If for an appropriate constant c, we show that this equation has a nontrivial solution.
Mathematics Subject Classification: 35B33 / 35J65 / 35Q55
Key words: Linking / Schrödinger equations / critical Sobolev exponent.
© EDP Sciences, SMAI, 2003