Solvability of second-order uniformly elliptic inequalities involving demicontinuous -dissipative operators and applications to generalized population models
College of Mathematics and Statistics, Sichuan University of Science and Engineering, 643000, Zigong, Sichuan, People’s Republic of China
2 South Sichuan Center for Applied Mathematics, and Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, 643000, Zigong, Sichuan, People’s Republic of China
3 Instituto de Matematicas, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain
Accepted: 23 September 2020
Published online: 25 February 2021
Based on a new developed theory for variational inequalities, the purpose of this article is to investigate existence and uniqueness of nonzero positive weak solutions for a class of general second-order uniformly elliptic inequalities with demicontinuous -dissipative operators in reflexive smooth Banach spaces and a generalized second-order elliptic inequality, which are often regarded as some conditions allowing the species to survive in biology or ecological context with heterogeneous character. Further, we also discuss existence of eigenvalues for the uniformly elliptic inequality and present a generalized population model arising in ecological context to verify the availability and significance of our main results. Finally, we describe two kinds of open questions, which are future work of our research.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021