Opuscula Math. 39, no. 2 (2019), 131-144
https://doi.org/10.7494/OpMath.2019.39.2.131

Opuscula Mathematica

# On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative

Michał Bełdziński
Marek Galewski

Abstract. In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.

Keywords: diffeomorphism, uniqueness, non-potential problems, variational methods, monotone methods, Palais-Smale condition.

Mathematics Subject Classification: 34A12, 47H30, 47J07.

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• Communicated by Vicentiu D. Radulescu.
• Revised: 2018-11-05.
• Accepted: 2018-11-06.
• Published online: 2018-12-07.