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Multiplicity results for some nonlinear elliptic problems

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

Kuan-Ju Chen
Kuan-Ju Chen
Affiliation:
Department of Applied Science, Chinese Naval Academy, 669 Jiun Shiaw Road Kaohsiung, Taiwan, R.O.C., e-mail: Kuanju@mail.cna.edu.tw
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Abstract

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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 (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.

Keywords

Palais-Smale sequencehigher energy solutionupper half strip with a hole

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 247 - 268
Copyright
Copyright © Australian Mathematical Society 2004

References

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