J. Aust. Math. Soc.  76 (2004), 247-268
Multiplicity results for some nonlinear elliptic problems

Kuan-Ju Chen
  Department of Applied Science
  Chinese Naval Academy
  669 Jiun Shiaw Road
  Taiwan R.O.C.

In this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a $(\textit{PS})_c$-sequence with $c$ belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.
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