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weak-indefinite singularity

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Periodic solutions for a second-order differential equation with indefinite weak singularity
Part of
- Boundary value problems
- Qualitative theory
José Godoy, Manuel Zamora
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 5 / October 2019

Published online by Cambridge University Press:

15 January 2019, pp. 1135-1152

Print publication:

October 2019
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As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a T −periodic solution to the second-order differential equation
$${u}^{\prime \prime} = \displaystyle{{h(t)} \over {u^\lambda }}$$
are established. Here, h ∈ L(ℝ/Tℤ) is a piecewise-constant sign-changing function and the non-linear term presents a weak singularity at 0 (i.e. λ ∈ (0, 1)).