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In this paper we prove a generalization of the well known theorem of Krasnoselskii on the superposition operator in which the domain of Nemytskii's operator is a product space. We also give an application of this result.

In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasing norm-bounded sequence has a limit. We supply a counterexample, which shows that this property is essential and give a modification of obtained results for the space C(T), which does not possess this property.

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122 results in 49Jxx

On a generalization of Krasnoselskii's theorem

Existence and uniqueness of a solution for a minimization problem with a generic increasing function

49Jxx

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122 results in 49Jxx

On a generalization of Krasnoselskii's theorem

Existence and uniqueness of a solution for a minimization problem with a generic increasing function