Moser-Harnack inequality, Krasnosel'skii type fixed point theorems in cones and elliptic problems

Radu Precup

Abstract


Fixed point theorems of Krasnosel'skiń≠ type are obtained for the localization
of positive solutions in a set defined by means of the norm and of
a semi-norm. In applications to elliptic boundary value problems, the
semi-norm comes from the Moser-Harnack inequality for nonnegative
superharmonic functions whose use is crucial for the estimations from below.
The paper complements and gives a fixed point alternative approach to our
similar results recently established in the frame of critical point theory.
It also provides a new method for discussing the existence and multiplicity
of positive solutions to elliptic boundary value problems.

Keywords


Fixed point index; cone; elliptic equation; positive solution; Moser-Harnack inequality

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