Interface Problems for Quasilinear Elliptic Equations

On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations

We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem  −div (|∇u|∇u) = λa(x)|u|u+ b(x)|u|u, x ∈ Ω, ∂u ∂n = 0, x ∈ ∂Ω , where Ω is a smooth bounded domain in Rn, b changes sign, 1 < p < N , 1 < γ < Np/(N − p) and γ 6= p. We prove that (i) if ∫ Ω a(x) dx 6= 0 and b satisfies another integral condition, then there exists some λ∗ suc...

Large Solutions for Quasilinear Elliptic Equations

On Quasilinear Elliptic Equations in Ir

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.

Anisotropic quasilinear elliptic equations with variable exponent

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.

Positive Solutions of Quasilinear Elliptic Equations

(1.2) { −∆pu = λa(x)|u|p−2u, u ∈ D 0 (Ω), has the least eigenvalue λ1 > 0 with a positive eigenfunction e1 and λ1 is the only eigenvalue having this property (cf. Proposition 3.1). This gives us a possibility to study the existence of an unbounded branch of positive solutions bifurcating from (λ1, 0). When Ω is bounded, the result is well-known, we refer to the survey article of Amann [2] and t...