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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)

- Zhanping Liang, Fuyi Li, Junping Shi
- 2014

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)

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