2 results
Periodic solutions for indefinite singular perturbations of the relativistic acceleration
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 4 / August 2018
- Published online by Cambridge University Press:
- 22 June 2018, pp. 703-712
- Print publication:
- August 2018
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- Article
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Using the Leray–Schauder degree, we study the existence of solutions for the following periodic differential equation with relativistic acceleration and singular nonlinearity:
where μ > 1 and the weight h: [0, T] → ℝ is a continuous sign-changing function. There are no a priori estimates on the set of positive solutions (a condition used in general to apply the Leray–Schauder degree), and we prove that no solution of the equation appears on the boundary of an unbounded open set during the deformation to an autonomous problem.
Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problem on the Sphere
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 173-190
- Print publication:
- 01 February 2018
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We study a second-order ordinary differential equation coming from the Kepler problem on
${{\mathbb{S}}^{2}}$. The forcing term under consideration is a piecewise constant with singular nonlinearity that changes sign. We establish necessary and sufficient conditions to the existence and multiplicity of 
$T$-periodic solutions.
