Hiroyuki Usami

Some oscillation theorems for a class of quasilinear elliptic equations

Oscillation criteria are obtained for quasilinear elliptic equations of the form (E)below. We are mainly interested in the case where the coefficient function oscillates near infinity. Generalized Riccati inequalities are employed to establish our results.

Nonexistence results of positive entire solutions for quasilinear elliptic inequalities

This paper treats the quasilinear elliptic inequality div(jDujm 2Du) 1⁄2 p(x)uõÒ x 2 RN Ò where N 1⁄2 2, m Ù 1, õ Ù m 1, and p:RN ! (0Ò1) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When p has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results. Received by the editors January 4, 1996. AMS subject classification: 35J70, 35B05. c Canadian Mathematical Society 1997. 244

Asymptotic forms of positive solutions of third-order Emden–Fowler equations

Abstract We obtain asymptotic forms of positive solutions of third-order Emden–Fowler equations. These results improve earlier results for asymptotic behavior of positive solutions considerably.