Standing waves for quasilinear Schröinger equations with indefinite potentials

Original · EN

We consider quasilinear Schrödinger equations in Rⁿ of the form% -Δu+V(x)u-uΔ(u²)=g(u),% where g(u) is 4-superlinear. Unlike all known results in the literature, the Schrödinger operator -Δ+V is allowed to be indefinite, hence the variational functional does not satisfy the mountain pass geometry. By a local linking argument and Morse theory, we obtain a nontrivial solution for the problem. In case that g is odd, we get an unbounded sequence of solutions.