Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity
نویسندگان
چکیده
منابع مشابه
Entire Solutions for a Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity∗
We investigate entire radial solutions of the semilinear biharmonic equation ∆u = λ exp(u) in Rn, n ≥ 5, λ > 0 being a parameter. We show that singular radial solutions of the corresponding Dirichlet problem in the unit ball cannot be extended as solutions of the equation to the whole of Rn. In particular, they cannot be expanded as power series in the natural variable s = log |x|. Next, we pro...
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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: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2006.05.015