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Existence theorems on the Dirichlet problem for the equation Δu + f(x, u)=0
Published online by Cambridge University Press: 20 January 2009
Abstract
In this note we consider the Dirichlet problem Δu + f(x, u)=0 in Ω, u = 0 on ∂Ω here Ω is a bounded domain in ℝn(n≧3), with smooth boundary ∂Ω. We prove the existence of strong solutions to the previous problem, which are positive if f satisfies a suitable condition. As a consequence we find that the problem with , may have positive solutions even if g is not a lower-order perturbation of Next We examine the case .
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 31 - 36
- Copyright
- Copyright © Edinburgh Mathematical Society 1996