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New variational principle and duality for an abstract semilinear Dirichlet problem

Marek Galewski (2003)

Annales Polonici Mathematici

A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇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.

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