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AUTHORS PREFACE v
ANALYSIS IN LINEAR SPACES
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abstract function according to Theorem arbitrary assume Banach space bifurcation point bounded set boundedness completely continuous conditionally critical points conditions of Theorem continuous functional continuous operator converges weakly corresponding proper definition denote Euclidean space Ex into Ey existence finite dimensional following conditions Frechet differential functional f grad gradient Hammerstein operator Hence holds hyperboloid inequality infimum integral operator kernel linear Gateaux differential linear operator Lipschitz condition Lusternik measurable function Nauk Nemytsky operator Newton's method nonlinear operators norm obtain operator F point x0 positive number potential operator preceding theorem principal square root proof of Theorem proper elements proper functions proper numbers proper values proves the theorem quasi-negative real Hilbert space region V0 remark satisfies a Lipschitz satisfies the condition self-adjoint operator solution space H Stieltjes integral strongly continuous subspace Suppose supremum topological product uniformly continuous vector-functions weakly closed weakly compact weakly continuous weakly lower semi-continuous zero