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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… (More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t The existence of a positive solution to a… (More)
a r t i c l e i n f o a b s t r a c t The existence of positive solutions depending on a nonnegative parameter λ to Kirchhoff type problems with zero mass is proved by using variational method, and the new result does not require usual compactness conditions. A priori estimate and a Pohozaev type identity are used to obtain the bounded Palais–Smale… (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 asymptot-ically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap… (More)
In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.
The existence of positive solutions to Schrödinger–Poisson type systems in R 3 with critically growing nonlocal term is proved by using variational method which does not require usual compactness conditions. A key ingredient of the proof is a new Brézis–Lieb type convergence result.