Morse theory for a fourth order elliptic equation with exponential nonlinearity

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Morse theory for a fourth order elliptic equation with exponential nonlinearity

Given a Hilbert space (H, 〈·, ·〉), and interval Λ ⊂ (0, +∞) and a map K ∈ C(H,R) whose gradient is a compact mapping, we consider the family of functionals of the type: I(λ, u) = 1 2 〈u, u〉 − λK(u), (λ, u) ∈ Λ×H. As already observed by many authors, for the functionals we are dealing with the (PS) condition may fail under just this assumptions. Nevertheless, by using a recent deformation Lemma ...

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ژورنال

عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA

سال: 2010

ISSN: 1021-9722,1420-9004

DOI: 10.1007/s00030-010-0082-1