Entire large positive radial symmetry solutions for combined quasilinear elliptic system

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...

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 ...

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Large Solutions for Quasilinear Elliptic Equations

Radial Symmetry of Positive Solutions of Nonlinear Elliptic Equations

We study the radial symmetry and asymptotic behavior at x = 1 of positive solutions of u = '(jxj)u ; x 2 IR n and jxj large () where > 1 and '(r) is positive and continuous for r large. In particular we give conditions on ' which guarantee that each positive solution of () satisses u(x) u(jxj) ! 1 as jxj ! 1 where u(r) is the average of u on the sphere jxj = r.