Volume 5, Issue 3
On the Existence of Positive Solutions of Quasilinear Elliptic Equations with Mixed Boundary Conditions

J. Part. Diff. Eq.,5(1992),pp.61-71

Published online: 1992-05

Preview Purchase PDF 0 3349
Export citation

Cited by

• Abstract
In this paper, the existence of positive solutions for the mixed boundary problem of quasilinear elliptic equation {-div (|∇u|^{p-2}∇u) = |u|^{p^∗-2}u + f(x, u), \quad u > 0, \quad x ∈ Ω u|_Γ_0 = 0, \frac{∂u}{∂\overrightarrow{n}}|_Γ_1 = 0 is obtained, where Ω is a bounded smooth domain in R^N, ∂Ω = \overrightarrow{Γ}_0 ∪ \overrightarrow{Γ}_1, 2 ≤ p < N, p^∗ = \frac{Np}{N-p}, Γ_0 and Γ_1 are disjoint open subsets of ∂Ω.
• Keywords

Critical point theory quasilinear elliptic equation mixed boundary condition isoperimetric constant