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CONTENTSIntroduction......................................................................................................5I. Preliminaries1. Strong convergence and weak convergence in Banach spaces..................72. Compact and weakly compact sets in Banach spaces.................................73. Weakly compact sets in the space of integrable functions...........................84. Compact sets in the space of continuous functions.....................................95. Basic integral and...

This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in $\Omega \subset {ℝ}^n$, $u=Du=...=D^{m-1}u$ on ∂Ω in the Sobolev space $W_0^{m,2}\left(\Omega \right)$, where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.