On nonnegative radial entire solutions of second order quasilinear elliptic systems

Solutions to general quasilinear elliptic second order problems

We study the second order quasilinear equation (1) Qu = f(x; u; D 1 u; :::; D n u) with Dirichlet conditions. We obtain existence and uniqueness results in the Sobolev Space W 2;p. We also prove that, in certain cases, the set of solutions of (1) is a connected subset of W 2;p .

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...

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Existence of Entire Solutions for Quasilinear Elliptic Systems under Keller-Osserman Condition

In this paper, we study the existence of entire solutions for the following elliptic system △mu = p(x)f(v),△lv = q(x)g(u), x ∈ R, where 1 < m, l < ∞, f, g are continuous and non-decreasing on [0,∞), satisfy f(t) > 0, g(t) > 0 for all t > 0 and the Keller-Osserman condition. We establish conditions on p and q that are necessary for the existence of positive solutions, bounded and unbounded, of t...

Remarks on entire solutions for two fourth order elliptic problems

We are interested in entire solutions for the semilinear biharmonic equation ∆u = f(u) in R , where f(u) = e or −u−p (p > 0). For the exponential case, we prove that for the polyharmonic problem ∆u = e with positive integer m, any classical entire solution verifies ∆2m−1u < 0, this completes the results in [6, 14]; we obtain also a refined asymptotic expansion of radial separatrix solution to ∆...