Positive weak solutions of uniformly elliptic inequalities and applications to population models

References

• Le VK, Schmitt K. On boundary value problems for degenerate quasilinear elliptic equations and inequalities. J Differ Equ. 1998;144:170–218.
   Web of Science ®Google Scholar
• Lan KQ. A variational inequality theory in reflexive smooth Banach spaces and applications to p-Laplacian elliptic inequalities. Nonlinear Anal. 2015;113:71–86.
   Web of Science ®Google Scholar
• Lan KQ, Zhang ZT. Nonzero positive weak solutions of systems of p-Laplace equations. J Math Anal Appl. 2012;394(2):581–591.
   Web of Science ®Google Scholar
• Anh CT, My BK. Existence of solutions to Δλ-Laplace equations without the Ambrosetti–Rabinowitz condition. Complex Var Elliptic Equ. 2016;61(1):137–150.
   Web of Science ®Google Scholar
• Shigesada N, Kawasaki K. Biological invasions: theory and practice. Oxford: Oxford University Press; 1997. (Oxford Series in Ecology and Evolution).
   Google Scholar
• Lan KQ. A variational inequality theory for demicontinuous S-contractive maps with applications to semilinear elliptic inequalities. J Differ Equ. 2009;246(3):909–928.
   Web of Science ®Google Scholar
• Medeiros ES, Severo UB, Silva Elves AB. An elliptic equation with indefinite nonlinearities and exponential critical growth in R2. Ann Sc Norm Super Pisa Cl Sci. 2019;19(2):473–507.
   Google Scholar
• Bordoni S, Filippucci R, Pucci P. Nonlinear elliptic inequalities with gradient terms on the Heisenberg group. Nonlinear Anal. 2015;121:262–279.
   Web of Science ®Google Scholar
• Lan HY, Nieto JJ. On a system of semilinear elliptic coupled inequalities for S-contractive type involving demicontinuous operators and constant harvesting. Dynam Syst Appl. 2019;28(3):625–649.
   Web of Science ®Google Scholar
• Kon'kov AA. On properties of solutions of quasilinear second-order elliptic inequalities. Nonlinear Anal. 2015;123-124:89–114.
   Web of Science ®Google Scholar
• Yang ZD, Miao Q. Bifurcation results to some quasilinear differential equation systems. Chaos Solitons Fractals. 2009;42(3):1914–1925.
   Web of Science ®Google Scholar
• Ghergu M, Karageorgis P, Singh G. Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms. J Differ Equ. 2020;268(10):6033–6066.
   Web of Science ®Google Scholar
• Luyen DT, Tri NM. On the existence of multiple solutions to boundary value problems for semilinear elliptic degenerate operators. Complex Var Elliptic Equ. 2019;64(6):1050–1066.
   Web of Science ®Google Scholar
• Kirane M, Nabana E. A nonexistence result for a system of quasilinear degenerate elliptic inequalities in a half-space. Electron J Differ Equ. 2002;56:1–11.
   Google Scholar
• Lan KQ, Webb JRL. Variational inequalities and fixed point theorems for PM-maps. J Math Anal Appl. 1998;224:102–116.
   Web of Science ®Google Scholar
• Lan KQ. A fixed point theory for weakly inward S-contractive maps. Nonlinear Anal. 2001;45(2):189–201.
   Web of Science ®Google Scholar
• Browder FE. Fixed point theory and nonlinear problems. Bull Amer Math Soc. 1983;9:1–39.
   Web of Science ®Google Scholar
• Karamardian S. Generalized complementarity problem. J Optim Theory Appl. 1971;8:161–168.
   Google Scholar
• Murray JD. Mathematical biology II: spatial models and biomedical applications. 3rd ed. New York: Springer-Verlag; 2003. (Interdisciplinary Applied Mathematics; 18).
   Google Scholar
• Hamel F, Roques L. Persistence and propagation in periodic reaction-diffusion models. Tamkang J Math. 2014;45(3):217–228.
   Google Scholar
• Ghergu M, Rǎdulescu Vicenţiu D. Nonlinear PDEs: mathematical models in biology, chemistry and population genetics, with a foreword by Viorel Barbu. Heidelberg: Springer; 2012. (Springer Monographs in Mathematics).
   Google Scholar
• Berestycki H, Hamel F, Roques L. Analysis of the periodically fragmented environment model: I-species persistence. J Math Biol. 2005;51(1):75–113.
   PubMed Web of Science ®Google Scholar
• Kinezaki N, Kawasaki K, Shigesada N. The effect of the spatial configuration of habitat fragmentation on invasive spread. Theoret Population Biol. 2010;78(4):298–308.
   PubMed Web of Science ®Google Scholar
• Tolksdorf P. On the Dirichlet problem for quasilinear equations in domains with conical boundary points. Comm Partial Differ Equ. 1983;8(7):773–817.
   Web of Science ®Google Scholar
• Istratescu VI. Fixed point theory. Dordrecht : Reidel Publishing Company; 1981.
   Google Scholar
• Ôtani M, Teshima T. On the first eigenvalue of some qualisilinear elliptic equations. Proc Japan Acad Ser A. 1988;64:8–10.
   Google Scholar
• Suzuki K. The first boundary value problem and the first eigenvalue problem for the elliptic equations degenerate on the boundary. Publ Res Inst Math Sci Ser A. 1967;3:299–335.
   Google Scholar
• Fisher RA. The advance of advantageous genes. Ann Eugenics. 1937;7:335–369.
   Google Scholar
• Conway E, Gardner R, Smoller J. Stability and bifurcation of steady-state solutions for predator-prey equations. Adv Appl Math. 1982;3(3):288–334.
   Google Scholar
• Dancer EN. On positive solutions of some pairs of differential equations. Trans Amer Math Soc. 1984;284(2):729–743.
   Web of Science ®Google Scholar
• Rasouli SH. On a population model with nonlinear boundary conditions arising in ecosystems. Bull Belg Math Soc Simon Stevin. 2019;26(1):63–69.
   Web of Science ®Google Scholar
• Goddard JII, Shivaji R. Diffusive logistic equation with constant yield harvesting and negative density dependent emigration on the boundary. J Math Anal Appl. 2014;414(2):561–573.
   Web of Science ®Google Scholar