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https://doi.org/10.7494/OpMath.202509181

 
Opuscula Mathematica

Radial solutions for a Neumann elliptic system with quadratic growth in the gradient

Filomena Cianciaruso
Paolamaria Pietramala

Abstract. We prove the existence of multiple positive solutions for elliptic systems with linear boundary conditions of Neumann type. We suppose that the nonlinearities grow quadratically with respect to gradient. A key step is to obtain a priori bound on the derivatives by using a Gronwall-type inequality. Our approach is topological and relies on the fixed point index.

Keywords: elliptic system, annular domain, radial solution, fixed point index, linear Neumann boundary conditions, Gronwall inequality.

Mathematics Subject Classification: 35B07, 34B18, 35J57, 47H10.

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  • Paolamaria Pietramala (corresponding author)
  • ORCID iD https://orcid.org/0000-0002-7435-9767
  • University of Calabria, Department of Mathematics and Computer Sciences, 87036 Rende, Cosenza, Italy
  • Communicated by Marek Galewski.
  • Received: 2025-06-30.
  • Revised: 2025-09-11.
  • Accepted: 2025-09-18.
  • Published online: 2026-03-18.
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