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non-trivial solutions

Proceedings of the Edinburgh Mathematical Society (1)

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Three non-trivial solutions for not necessarily coercive p-Laplacian equations
Part of
- Elliptic equations and systems
Shouchuan Hu, Nikolas S. Papageorgiou
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 3 / October 2009

Published online by Cambridge University Press:

23 September 2009, pp. 679-688
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We consider the existence of three non-trivial smooth solutions for nonlinear elliptic problems driven by the p-Laplacian. Using variational arguments, coupled with the method of upper and lower solutions, critical groups and suitable truncation techniques, we produce three non-trivial smooth solutions, two of which have constant sign. The hypotheses incorporate both coercive and non-coercive problems in our framework of analysis.