Online First version
https://doi.org/10.7494/OpMath.202603081

 
Opuscula Mathematica

Solutions to second-order nonlocal evolution equations governed by non-autonomous forms

Sajid Ullah
Vittorio Colao

Abstract. Our main contributions include proving sufficient conditions for the existence of solution to a second order problem with nonzero nonlocal initial conditions, and providing a comprehensive analysis using fundamental solutions and fixed-point techniques. The theoretical results are illustrated through applications to partial differential equations, including vibrating viscoelastic membranes with time-dependent material properties and nonlocal memory effects.

Keywords: non-autonomous evolution equations, fundamental solution, nonlocal conditions, sesquilinear forms, fixed point.

Mathematics Subject Classification: 35L15, 35B65, 47H10, 35R09.

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  • Sajid Ullah (corresponding author)
  • ORCID iD https://orcid.org/0009-0008-9486-7110
  • University of Calabria, Department of Mathematics and Computer Science, Ponte P. Bucci, 30B, Arcavacata di Rende (CS), Italy
  • Communicated by Marek Galewski.
  • Received: 2025-10-29.
  • Revised: 2026-03-04.
  • Accepted: 2026-03-08.
  • Published online: 2026-04-10.
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