We show that the problem at critical growth, involving the 1-Laplace operator and obtained by relaxation of − 1 u = λ|u| −1 u + |u| 1 * −2 u, admits a nontrivial solution u ∈ BV ( ) for any λ ≥ λ 1 . Nonstandard linking structures, for the associated functional, are recognized.
Mathematics Subject Classification (2000) 58E05 · 35J65
We prove the existence of three distinct nontrivial solutions for a class of semilinear elliptic variational inequalities involving a superlinear nonlinearity. The approach is variational and is based on linking and ∇-theorems. Some nonstandard adaptations are required to overcome the lack of the Palais-Smale condition.
In this paper we state some existence results for the semilinear elliptic equation −∆u(x) − λu(x) = W (x)f (u) where W (x) is a function possibly changing sign , f has superlinear growth and λ is a positive real parameter. We discuss both the cases of subcritical and critical growth for f, and prove the existence of Linking type solutions.
This paper deals with the problem of finding positive solutions to the equation −Δu = g(x, u) on a bounded domain Ω, with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem.2000 Mathematics Subject Classification: 35J20, 35J65.
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