Abstract
In this paper we deal with the existence of critical points of functional defined on the Sobolev space W01,p(Ω), p>1, by $$J(u) = \int\limits_\Omega {\vartheta (x,u,Du)dx,} {\text{ }}$$ where Ω is a bounded, open subset of ℝN. Even for very simple examples in ℝN the differentiability of J(u) can fail. To overcome this difficulty we prove a suitable version of the Ambrosetti-Rabinowitz Mountain Pass Theorem applicable to functionals which are not differentiable in all directions. Existence and multiplicity of nonnegative critical points are also studied through the use of this theorem.
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