Abstract

associated with .G! is defined for all u, v of some Sobolev space V = Wt*ysZ), 1 , 0 (t E R); no restriction on its growth is made. If the form a(v, v) + snp(v) v dx (v E C,“(Q)) is coercive, we prove that the Dirichlet problem for the equation &U + p(u) = f has a variational solution for each f E V*. Boundary-value problems for this type of equation were already investigated in our previous paper [5]. As an application of abstract existence theorems for a new class of mappings of monotone type we obtained there

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