Pacific Journal of Mathematics 202 247-255 Apr 2016

This paper treats the second order semilinear elliptic systems of the form δu = p(x)να, δν = q(x)uβ, x ∈ RN where α, β > 0 are constants satisfying αβ > 1, and p, q ∈ C(RN; (0, ∞)). We obtain a Liouville type theorem for non-negative entire soluti...

Proceedings of the Royal Society of Edinburgh Section A: Mathematics 139 1071-1089 Oct 2009

We show how one-dimensional generalized Riccati-type inequalities can be employed to analyse asymptotic behaviour of solutions of elliptic problems. We give Liouville-type theorems as well as necessary conditions for the existence of solutions of ...

Nonlinear Analysis, Theory, Methods and Applications 68 1627-1639

In this paper we consider positive solutions of second order quasilinear ordinary differential equations with singular nonlinearities. We obtain asymptotic equivalence theorems for asymptotically superlinear solutions and decaying solutions. By us...

Bulletin of the London Mathematical Society 42 420-428

We consider quasilinear ordinary differential equations with sub-homogeneity near infinity. A necessary and sufficient condition is obtained for the equations to have slowly decaying positive solutions. Asymptotic forms of such positive solutions ...

1.We consider second-order quasilinear ordinary differential equations which can be regarded as generalization of the Emden-Fowler equation. We determine asymptotic forms of every positive solutions. We also establish uniqueness of several types o...

(1) Quasilinear ODEs of seond-order, which are generalizations of Emden's equation, are considered. Asymptotic representations of positive solutions are obtained explicitly. When nonlinear terms have singularities at the origin, uniqueness of deca...

(1) Eigenvalue Problems of Elliptic Equations : Two-parameter eigenvalue problems for semilinear elliptic equations are studied. We establish asymptotic properties of (variational) eigenvalues and eigenfunctions. Two-parameter Ambrosetti-Prodi pro...

(1) Oscillation criteria for elliptic equations : Effective oscillation criteria are established for second-order quasilinear elliptic equations whose leading terms are degenerate Laplacians. Our method is based on comparison principles and asympt...