Nontrivial Solutions of a Class of Quasilinear Elliptic Problems Involving Critical Exponents

Abstract

In this paper we deal with the following class of quasilinear elliptic problems in radial form

$$ \left\{ {\begin{array}{*{20}{c}} { - {{\left( {{r^\alpha }{{\left| {u'} \right|}^\beta }u'} \right)}^\prime } = \lambda {r^\delta }{{\left| u \right|}^\beta }u + {r^\gamma }{{\left| u \right|}^{q - 2}} in \left( {0,R} \right)} \\ {u\left( R \right) = u'\left( 0 \right) = 0} \end{array}} \right. $$

(P)

where a, ß, (5,-y, q are given real numbers, A > 0 is a parameter and 0 < R <∞.