Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities
Published online by Cambridge University Press: 30 January 2012
Abstract
We study the existence and multiplicity of positive solutions for the Dirichlet problem
where λ > 0, 1 < q < 2, p = 2* = 2N/(N − 2), 0 ε Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on . Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 115 - 135
- Copyright
- Copyright © Royal Society of Edinburgh 2012
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