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Abstract. In this paper we improve Mountain
Pass Theorem and Saddle Point Theorem. Our results only require that the
functionals belong to C1w(E) instead of C1(E), where C1w(E) is the set of functionals that
are weakly continuously differentiable on the Banach space E. An application is the existence
of infinitely many generalized solutions to a nonuniformly nonlinear
elliptic equation of the form -div(a(x, u)) = f(x, u) in Ω with u  (Ω). Here a satisfies |a(x,ξ)|  c0
h(x)(1 + |ξ|p-1)
for any ξ in Rn, a.e.  ,
where  ).
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