A remark on the existence and multiplicity result for a nonlinear elliptic problem involving the p-Laplacian

Afrouzi, G. A.; Rasouli, S. H.

doi:10.1007/s00030-009-0031-z

Cited by 5 publications

(1 citation statement)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, several authors have used the Nehari manifold and fibering maps (i.e., maps of the form t −→ J λ (tu) where J λ is the Euler function associated with the equation) to solve semilinear and quasilinear problems (see [1][2][3]9,[11][12][13][14]17,[23][24][25][26]). By the fibering method, Drabek and Pohozaev [17], Bozhkov and Mitidieri [9] studied, respectively, the existence of multiple solution to a p-Laplacian single equation and ( p, q)-Laplacian system.…”

Section: Introductionmentioning

confidence: 99%

A variational approach to a quasilinear multiparameter elliptic system involving the p-Laplacian and nonlinear boundary condition

2012

Self Cite

View full text Add to dashboard Cite

− p u + m(x) |u| p−2 u = α α+β |u| α−2 u |v| β , x ∈ , − p v + m(x) |v| p−2 v = β α+β |u| α |v| β−2 v, x ∈ , |∇u| p−2 ∂u ∂n = λ a(x)|u| γ −2 u, |∇v| p−2 ∂v ∂n = μ b(x)|v| γ −2 v, x ∈ ∂. Here p denotes the p-Laplacian operator defined by p z = div (|∇z| p−2 ∇z), p > 2, ⊂ R N is a bounded domain with smooth boundary, α > 1, β > 1, 2 < α + β < p < γ < p * (p * = pN N − p if N > p, p * = ∞ if N ≤ p), ∂ ∂n is the outer normal derivative, (λ, μ) ∈ R 2 \{(0, 0)}, the weight m(x) is a positive bounded function, and a(x), b(x) ∈ C(∂) are functions which change sign in .

show abstract