The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type
نویسنده
چکیده
1 1 , , 0, , r s p u u h x u dx g x u dx x u x + + −∆ = + ∈ Ω = ∈ ∂Ω () 1, 0 p W Ω () () () 1 1 , 0. r s p u x h x u dx g x u dx in u on + + −∆ = + Ω = ∂Ω () E () () 1 1 / r p s Np N p N p < < − < < − + − () () () 0 0 r h L L C ∞ ∈ Ω Ω Ω 0 1 1 1, r r p * + + = ()() 0. 1 Np r Np r N p = − + − () () 0 s g L L ∞ ∈ Ω Ω 0 1 1 1, s s p * + + = ()() 0 ,. 1 Np Np s p Np s N p N p * = = − + − − () 1, 0 p X W = Ω () 0 C ∞ Ω () 1. p p X u u dx Ω = ∇ ∫ () () () 1 1 1 1 1. 1 p s r J u u dx g x u dx p s h x u dx r Abstract: In this paper we prove the existence of positive solutions for a class of quasilinear elliptic equations of the form: in where is a real parameter, is a bounded domain with smooth boundary in R , N 3. and1< r < N p-1 < s < (Np-N + p) / (N-P).
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