Titlebook: Critical Point Theory; Sandwich and Linking Martin Schechter Book 2020 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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Let . be a closed, separable subspace of a Hilbert space ..We can define a new norm |.|. satisfying |.|. ≤∥.∥, ∀. ∈ . and such that the topology induced by this norm is equivalent to the weak topology of . on bounded subsets of .. This can be done as follows: Let {..} be an orthonormal basis for .. Define

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We now consider some applications of the materials presented in Chaps. .–.. We wish to show how powerful these methods are in obtaining results better than those given by other methods. In Chaps. 7–. we deal with some problems involving Schrödinger equations.

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Wortgeschichten aus alten Gemeinden,We consider the system . where . is a map from . = [0, .] to . such that each component ..(.) is a periodic function in .. with period ., and the function . (., .) = . (., .., ⋯ , ..) is continuous from . to . with . For each . the function . (., .) is periodic in . with period ..

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Wortgeschichten aus alten Gemeinden,Consider the problem . where . is a bounded domain whose boundary is a smooth manifold, and .(., .) is a continuous function on . The following theorem will be a corollary of the results of this chapter.

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https://doi.org/10.1007/978-3-663-02981-6In this chapter we show how monotonicity methods combined with infinite dimensional sandwich pairs can be used to solve very general systems of equations whether or not they are semibounded.

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https://doi.org/10.1007/978-3-663-02981-6In this chapter we study periodic solutions of the Dirichlet problem for the semilinear wave equation:

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