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2 results

  • Rotating periodic solutions for p-Laplacian differential systems

  • Part of
  • Tiefeng Ye, Wenbin Liu, Tengfei Shen
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 5 / October 2024
    Published online by Cambridge University Press:
    30 August 2023, pp. 1604-1633
    Print publication:
    October 2024
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  • In this paper, we study existence of rotating periodic solutions for p-Laplacian differential systems. We first build a new continuation theorem by topological degree, and then obtain the existence of rotating periodic solutions for two kinds of p-Laplacian differential systems via this continuation theorem, extend some existing relevant results.

  • Periodic solutions for indefinite singular perturbations of the relativistic acceleration

  • Part of
  • Cristian Bereanu, Manuel Zamora
  • 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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  • 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.