Large Solutions of Quasilinear Elliptic System of Competitive Type: Existence and Asymptotic Behavior

Large Solutions of Quasilinear Elliptic System of Competitive Type: Existence and Asymptotic Behavior

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Asymptotic Behavior of Positive Solutions of Some Quasilinear Elliptic Problems

We discuss the asymptotic behavior of positive solutions of the quasilinear elliptic problem −∆pu = au p−1 − b(x)u, u|∂Ω = 0 as q → p − 1 + 0 and as q → ∞ via a scale argument. Here ∆p is the p-Laplacian with 1 < p < ∞ and q > p−1. If p = 2, such problems arise in population dynamics. Our main results generalize the results for p = 2, but some technical difficulties arising from the nonlinear d...

Entire Large Solutions of Quasilinear Elliptic Equations of Mixed Type

In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation   2 | | = ( ) ( ) ( ) ( ) m div u u p x f u q x g u     are established, where 2 m  , f and g are nondecreasing and vanish at the origin. The locally H older continuous functions p and q are nonnegative. We extend results previously obtained for special cases of f a...

EXISTENCE OF POSITIVE SOLUTIONS FOR A QUASILINEAR ELLIPTIC SYSTEM OF p–KIRCHHOFF TYPE

In this paper, we consider the existence of positive solutions to the following p Kirchhoff-type system ⎧⎪⎨⎪⎪⎩ −M (∫ Ω |∇u|pdx ) Δpu = g(x)|u|q−2u+ α α+β |u|α−2u|v|β , x ∈Ω, −M (∫ Ω |∇u|pdx ) Δpv = h(x)|v|q−2v+ β α+β |u|α |v|β−2v, x ∈Ω, u = v = 0, x ∈ ∂Ω, where Ω is a bounded domain in RN , M(s) = a + bsk , Δpu = div(|∇u|p−2∇u) is the p Laplacian operator, α > 1 , β > 1 , 1 < p < q < α +β < p∗ ...