A generalization of compact operators and its application to the existence of local minima without convexity

A generalization of compact operators and its application to the existence of local minima without convexity

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Pablo Pedregal, Universidad de Castilla-La Mancha
Fine Hall 224

We will introduce a certain property for a continuous (non-linear) operator that allows for the existence of local minima for functionals when the derivative complies with such a condition, without the need to check either weak lower semicontinuity or convexity. It turns out that this property is a generalization of the standard compactness for a continuous, non-linear operator. We illustrate the relevance of this condition by applying it to several problems in one space dimension.