Asymptotic Behavior of Ground State Radial Solutions for -Laplacian Problems

Asymptotic Behavior of Ground State Solution for Hénon Type Systems

In this article, we investigate the asymptotic behavior of positive ground state solutions, as α→∞, for the following Hénon type system −∆u = 2p p+ q |x|αup−1vq , −∆v = 2q p+ q |x|αupvq−1, in B1(0) with zero boundary condition, where B1(0) ⊂ RN (N ≥ 3) is the unit ball centered at the origin, p, q > 1, p+ q < 2∗ = 2N/(N − 2). We show that both components of the ground solution pair (u, v) conce...

Positive radial solutions for p-Laplacian systems

The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1...

Existence and Asymptotic Behavior of Solutions for Weighted p(t)-Laplacian System Multipoint Boundary Value Problems in Half Line

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...

Multiplicity Results of Positive Radial Solutions for p-Laplacian Problems in Exterior Domains