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truncated functional

Proceedings of the Edinburgh Mathematical Society (1)

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Multiplicity theorems for semilinear elliptic problems depending on a parameter
Part of
- Elliptic equations and systems
- Variational problems in infinite-dimensional spaces
Alexandru Kristály, Nikolaos S. Papageorgiou
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009

Published online by Cambridge University Press:

02 February 2009, pp. 171-180
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We consider semilinear elliptic problems in which the right-hand-side nonlinearity depends on a parameter λ > 0. Two multiplicity results are presented, guaranteeing the existence of at least three non-trivial solutions for this kind of problem, when the parameter λ belongs to an interval (0,λ*). Our approach is based on variational techniques, truncation methods and critical groups. The first result incorporates as a special case problems with concave–convex nonlinearities, while the second one involves concave nonlinearities perturbed by an asymptotically linear nonlinearity at infinity.