On the existence of solutions to an inhomogeneous pantograph type equation with singular coefficients

Abstract

We establish the existence of solutions to an initial boundary value problem that involves a certain class of nonhomogeneous functional partial differential equations of the pantograph type with singular time dependent coefficients. The problem is motivated from a cell division equation. The techniques for solving such problems are rare due to the nonlocal term and the singularity in coefficients.

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Acknowledgements

We thank the referees for their valuable suggestions that led to improvements in the paper.

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Correspondence to A. A. Zaidi.

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Shah, S.T.H., Zaidi, A.A. On the existence of solutions to an inhomogeneous pantograph type equation with singular coefficients. J Elliptic Parabol Equ 6, 935–945 (2020). https://doi.org/10.1007/s41808-020-00089-3

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Keywords

  • Functional partial differential equations
  • Parabolic partial differential equations
  • Partial differential equations with singular coefficients

Mathematics Subject Classification

  • 35K20
  • 34K06
  • 35K67