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ANALYSIS IN LINEAR SPACES
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abstract function according to Theorem assume Banach space bifurcation point bounded set boundedness conditionally critical points conditions of Theorem continuous functional converges weakly corresponding proper definition denote Euclidean space Ex into Ey existence extreme point finite dimensional following conditions Frechet derivative functional f given grad gradient Hammerstein operator Hence holds hyperboloid inequality infimum integral operator kernel linear Gateaux differential linear operator Lipschitz condition llxll 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 remark satisfies a Lipschitz satisfies the condition self-adjoint operator solution space H Stieltjes integral strongly continuous subspace Suppose supremum topological product uniformly continuous variational methods vector-functions weakly closed weakly compact weakly continuous weakly lower semi-continuous zero