On the Convergence of Minimizers or Approximations to Nonlinear Elliptic Problems

Let Ω be a domain in Rn , J h be the energy functional on H (Ω) 1 0 for the semilinear equation -△u + u = u p−2 u + h(x) A group of local mathematicians has obtained a series of existence results and multiple solutions on various achieved domains for Sobolev subcritical constant. In this project, one intends to combine certain noncompact Krasnosel'skii type fixed point theorems to extend the above existence results to the quasilinear equation： -△u + u = u p−2 u + h(Du). In case Ω is bounded, there are various types of solutions to the quasilinear elliptic equations with quadratic growth in the gradient. For example Di (aij (u)Dj u) + a u 0 - Draij (u)Di (u)Dj (u) 2 1 - h = 0. We shall examine whether the approximating solutions constitute a Palais-Smale sequence and satisfy convergence conditions. From this point of view, one expects to derive further existence results for quasilinear problems.

Project ID:PA9308-1163
External Project ID:NSC93-2115-M182-002