Existence of Solutions for Quasilinear Elliptic Equations

Using variational methods we study the existence and multiplicity of solutions of the Dirichlet problem for the equation p py2 ydiv a =u .=u =u.sf x,u.. Q 1997 Academic Press 1. INTRODUCTION In this paper, we study the existence of solutions for the following class of quasilinear elliptic problems: p py2 ydiv a =u .=u =u/sf x,u. in V, us0 on­V, 1. where p)1, V is a bounded domain in RN with smooth boundary ­V, f : V=RªR is a Carath´eodory function with subcritical growth, that is, ry1 f x,u. Fc u qd , ;ugR, a.e. xgV, 2. 0 0 for some constants c0, d0)0, 1Fr-pU, where pUsNpr Nyp.if N)p; pUsq` if 1FNFp and a: RqªR is a continuous function * Work partially supported by CAPESrBrazil