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Multiple solutions for some quasilinear Neumann problems in exterior domains

Published online by Cambridge University Press:  18 September 2007

Tsing-San Hsu
Tsing-San Hsu
Affiliation:
Center for General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan, Republic of China (tshsu@mail.cgu.edu.tw)
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Abstract

In this paper, we show that if $K(x)$ satisfies suitable conditions, then the quasilinear Neumann problem $-\Delta_pu+|u|^{p-2}u=K(x)|u|^{q-2}u$ in an exterior domain $\varOmega$ has at least two solutions, of which one is a positive ground-state solution and one is a nodal solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 5 , October 2007 , pp. 1059 - 1071
Copyright
2007 Royal Society of Edinburgh

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