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Bounded positive solutions for diffusive logistic equations with unbounded distributed limitations

  • * Corresponding author: Jesús Ildefonso Díaz

    * Corresponding author: Jesús Ildefonso Díaz 

Dedicated to Georg Hetzer: Elegant mathematician and very good friend in his 75th

Partially supported the UCM Research Group MOMAT (ref. 910480) and the projects MTM2017-85449-P and PID2020-112517GB-I00 of the DGISPI, Spain

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  • We establish the existence of bounded very weak solutions to a large class of stationary diffusive logistic equations with weights by constructing suitable sub and supersolutions. This class of problems corresponds to the case in which the absorption term dominates over the forcing term. The case of simultaneous singular nonlinearities and singular weights is also considered. This shows that if limitations in the growth of a population are distributed and unbounded, but satisfy some mild integrability assumption in terms of the distance to the boundary, solutions can still be bounded. The results extend several papers in the literature.

    Mathematics Subject Classification: 92B05, 35D05, 35J60, 35J75.


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