MULTIPLE SOLUTIONS FOR A CLASS OF QUASILINEAR SCHRÖDINGER SYSTEM IN ℝ<sup>N</sup>
MULTIPLE SOLUTIONS FOR A CLASS OF QUASILINEAR SCHRÖDINGER SYSTEM IN ℝ<sup>N</sup>
This paper is concerned with the quasilinear <TEX>$Schr{\ddot{o}}dinger$</TEX> system <TEX>$$(0.1)\;\{-{\Delta}u+a(x)u-{\Delta}(u^2)u=Fu(u,v)+h(x)\;x{\in}{\mathbb{R}}^N,\\-{\Delta}v+b(x)v-{\Delta}(v^2)v=Fv(u,v)+g(x)\;x{\in}{\mathbb{R}}^N,$$</TEX> where <TEX>$N{\geq}3$</TEX>. The potential functions <TEX>$a(x),b(x){\in}L^{\infty}({\mathbb{R}}^N)$</TEX> are bounded in <TEX>${\mathbb{R}}^N$</TEX>. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).