Boundary blow-up rates of large solutions for quasilinear elliptic equations with convention terms

Boundary Blow–up Rates of Large Solutions for Quasilinear Elliptic Equations with Convention Terms

We use Karamata regular variation theory to study the exact asymptotic behavior of large solutions near the boundary to a class of quasilinear elliptic equations with convection terms ⎧⎨ ⎩ Δpu±|∇u|q(p−1) = b(x) f (u), x ∈Ω,

Boundary blow up solutions for fractional elliptic equations

In this article we study existence of boundary blow up solutions for some fractional elliptic equations including (−∆)u+ u = f in Ω, u = g on Ω, lim x∈Ω,x→∂Ω u(x) = ∞, where Ω is a bounded domain of class C2, α ∈ (0, 1) and the functions f : Ω → R and g : RN \ Ω̄ → R are continuous. We obtain existence of a solution u when the boundary value g blows up at the boundary and we get explosion rate f...

Existences and Boundary Behavior of Boundary Blow-up Solutions to Quasilinear Elliptic Systems with Singular Weights

Using the method of explosive sub and supper solution, the existence and boundary behavior of positive boundary blow up solutions for some quasilinear elliptic systems with singular weight function are obtained under more extensive conditions.

Large Solutions for Quasilinear Elliptic Equations

Large Solutions for an Elliptic System of Quasilinear Equations

In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the p-Laplacian defined by ∆pu = div(|∇u|p−2∇u), p > 1, and the exponents verify a, e > p − 1, b, c > 0 and (a − p + 1)(e − p + 1) ≥ bc. We analyze positive solutions in both components, providing necessary and ...