New variational principle and duality for an abstract semilinear Dirichlet problem

Volume 82 / 2003

Marek Galewski Annales Polonici Mathematici 82 (2003), 51-60 MSC: 35A15, 70G99. DOI: 10.4064/ap82-1-6


A new variational principle and duality for the problem $Lu=\nabla G(u) $ are provided, where $L$ is a positive definite and selfadjoint operator and $\nabla G$ is a continuous gradient mapping such that $G$ satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.


  • Marek GalewskiFaculty of Mathematics
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland

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