The 25-35 fragment of the amyloid β (Aβ) peptide is a naturally occurring proteolytic by-product of its larger parent molecule that retains the amyloid characteristics and toxicity of the full length parent molecule. Aggregation of this peptide occurs rapidly in aqueous solutions and thus characterization of its folding process is very difficult. In the present study, early stages of Aβ(25–35) ...

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

Under generic assumptions, we prove boundedness of Palais-Smale sequences relative to some geometric functional defined on H(M), where M is a four-dimensional manifold. Our analysis is useful to find critical points (via minimax arguments) of this functional, which give rise to conformal metrics of constant Q-curvature. The proof is based on a refined bubbling analysis, for which the main estim...

Let X be a real Banach space and Φ ∈ C 1 (X, R) a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence {u n } of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of u n from S for certain types of set S as n → ∞. Under our hypotheses we can ...

The main purpose of this paper is to establish a three critical points result without assuming the coercivity of the involved functional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then applied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions.

where Ω ⊂ R is a smooth domain with smooth boundary ∂Ω such that 0 Î Ω, Δpu = div(|∇u|∇u), 1 < p < N, μ < μ̄ = ( N−p p ), l >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on ̄, μ̄ = ( N−p p ) p is the best Hardy constant and p∗ = Np N−p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solu...