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In this paper, we discuss the existence of positive periodic solutions to the nonlinear differential equation u′′(t)+ a(t)u(t) = f (t, u(t)), t ∈ R, where a : R → [0,+∞) is an ω-periodic continuous function with a(t) ≡ 0, f : R × [0,+∞) → [0,+∞) is continuous and f (·, u) : R → [0,+∞) is also an ω-periodic function for each u ∈ [0,+∞). Using the fixed point(More)
MOTIVATION Glycosylation is a ubiquitous type of protein post-translational modification (PTM) in eukaryotic cells, which plays vital roles in various biological processes (BPs) such as cellular communication, ligand recognition and subcellular recognition. It is estimated that >50% of the entire human proteome is glycosylated. However, it is still a(More)
Existence and bifurcation of positive solutions to a Kirchhoff type equation ⎧⎪⎨ ⎪⎩ − ( a + b ∫ Ω |∇u|2 ) u= νf (x,u), in Ω, u= 0, on ∂Ω are considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap(More)
Summary Proteases are enzymes that specifically cleave the peptide backbone of their target proteins. As an important type of irreversible post-translational modification, protein cleavage underlies many key physiological processes. When dysregulated, proteases' actions are associated with numerous diseases. Many proteases are highly specific, cleaving only(More)