4
Fučík spectrum
4.1 Introduction
Let us recall some terminology concerning mappings between Hilbert spaces.
Definition 4.1.1 Let H, H′ be Hilbert spaces.
(i)  f : H → H′ is bounded if it maps bounded sets into bounded sets.  
(ii)  f : H → H′ is positive homogeneous of degree α > 0 if
Taking u = 0 and s = 0 gives f (0) = 0. When α = 1 we will simply say that f is positive homogeneous. 

(iii)  f : H → H is monotone if  
(iv)  f ∈ C(H, H) is a potential operator if there is a F ∈ C^{1}(H, ℝ), called a potential for f , such that
Replacing ... 
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