No abstract

Abstract. -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.1. -Introduction.In this paper we treat quasilinear elliptic equations of the formin an exterior domain t9 r R N, where x = (xi), Du = (au/axi). We note that the exponent of the leading term of (E) coincides with that of the nonlinear term. Such quasilinear equations are sometimes called half-linear equations. We always assume that N i> 2, m > 1, and a e C(~2). By a solution of (E) we mean a function u which is of class C 1 together with IDulm-~Du, and satisfies (E) near ~.DEFINITION. -(i) A nontrivial solution u of (E) (defined near ~ ) is called osciUatory ff the set {x e t9 N domu: u(x) = 0} is unbounded.

No abstract

No abstract

Oscillation criteria for fourth-order quasilinear ordinary differential equations are obtained. An application to binary semilinear elliptic systems is also given.