An indefinite and critical concave—convex-type equation
Published online by Cambridge University Press: 30 January 2013
Abstract
We analyse the multiplicity of non-negative solutions for the critical concave—convex-type equation
where Ω is a bounded domain of ℝN, 1 < r < p and λ > 0, and μ is a real parameter. Combining minimization on the underlying Nehari manifold with energy estimates, we show that, under suitable conditions on a and b, three non-negative solutions may exist when λ is positive and sufficiently small and μ is in a right neighbourhood of μ1, the first weighted eigenvalue of the p-Laplacian. To the best of our knowledge, our multiplicity result is new, even in the semi-linear case p = 2.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 1 , February 2013 , pp. 169 - 184
- Copyright
- Copyright © Royal Society of Edinburgh 2013
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